document.write( "Question 196896: I have a few problems I'm struggling with:\r
\n" ); document.write( "\n" ); document.write( "1: x^2 - 3x = -10 (directions say use quadratic formula, use radicals as needed).\r
\n" ); document.write( "\n" ); document.write( "2: (x+12)(x-8)(x+8)>0 (directions say to use one equality or compount equality)\r
\n" ); document.write( "\n" ); document.write( "3: 2x^2 - 5x +1 (evaluate polynomial for x= -4\r
\n" ); document.write( "\n" ); document.write( "4: (9x^8 - 3)(x^9 - 3) (use FOIL to find product)
\n" ); document.write( "I thank you in advance for time spent in helping with these problems \n" ); document.write( "

Algebra.Com's Answer #147630 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2-3x=-10\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2-3x%2B10=0\"$ Get all terms to the left side.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic in the form of $\"Ax%5E2%2BBx%2BC\"$ where $\"A=1\"$ , $\"B=-3\"$ , and $\"C=10\"$ \r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"$ Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29\"$ Plug in $\"A=1\"$ , $\"B=-3\"$ , and $\"C=10\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29\"$ Negate $\"-3\"$ to get $\"3\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+sqrt%28+9-4%281%29%2810%29+%29%29%2F%282%281%29%29\"$ Square $\"-3\"$ to get $\"9\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+sqrt%28+9-40+%29%29%2F%282%281%29%29\"$ Multiply $\"4%281%29%2810%29\"$ to get $\"40\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+sqrt%28+-31+%29%29%2F%282%281%29%29\"$ Subtract $\"40\"$ from $\"9\"$ to get $\"-31\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+sqrt%28+-31+%29%29%2F%282%29\"$ Multiply $\"2\"$ and $\"1\"$ to get $\"2\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283+%2B-+i%2Asqrt%2831%29%29%2F%282%29\"$ Simplify the square root \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%283%2Bi%2Asqrt%2831%29%29%2F%282%29\"$ or $\"x+=+%283-i%2Asqrt%2831%29%29%2F%282%29\"$ Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "So the answers are $\"x+=+%283%2Bi%2Asqrt%2831%29%29%2F%282%29\"$ or $\"x+=+%283-i%2Asqrt%2831%29%29%2F%282%29\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29=0\"$ Set the left side equal to zero\r
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\n" ); document.write( "\n" ); document.write( "Set each individual factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2B8=0\"$ , $\"x-8=0\"$ or $\"x%2B12=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Solve for x in each case:\r
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\n" ); document.write( "\n" ); document.write( " $\"x=-8\"$ , $\"x=8\"$ or $\"x=-12\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our critical values are $\"x=-8\"$ , $\"x=8\"$ and $\"x=-12\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now set up a number line and plot the critical values on the number line\r
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\n" ); document.write( "\n" ); document.write( " $\"number_line%28+600%2C+-15%2C+10%2C-8%2C8%2C-12%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So let's pick some test points that are near the critical values and evaluate them.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is less than $\"-12\"$ (notice how it's to the left of the leftmost endpoint):\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=-13\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-13%2B8%29%28-13-8%29%28-13%2B12%29%3E+0\"$ Plug in $\"x=-13\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"-105%3E+0\"$ Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between $\"-12\"$ and $\"-8\"$ :\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=-10\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%28-10%2B8%29%28-10-8%29%28-10%2B12%29%3E+0\"$ Plug in $\"x=-10\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"72%3E+0\"$ Evaluate and simplify the left side\r
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\n" ); document.write( "\n" ); document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r
\n" ); document.write( "\n" ); document.write( " So part our solution in interval notation is (

)\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is in between $\"-8\"$ and $\"8\"$ :\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%280%2B8%29%280-8%29%280%2B12%29%3E+0\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-768%3E+0\"$ Evaluate and simplify the left side\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the inequality is false, this means that the interval does not work. So this interval is not in our solution set and we can ignore it.\r
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\n" ); document.write( "\n" ); document.write( "Let's pick a test value that is greater than $\"8\"$ (notice how it's to the right of the rightmost endpoint):\r
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\n" ); document.write( "\n" ); document.write( "So let's pick $\"x=9\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B8%29%28x-8%29%28x%2B12%29%3E0\"$ Start with the given inequality\r
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\n" ); document.write( "\n" ); document.write( " $\"%289%2B8%29%289-8%29%289%2B12%29%3E+0\"$ Plug in $\"x=9\"$ \r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( " $\"357%3E+0\"$ Evaluate and simplify the left side\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Since the inequality is true, this means that the interval works. So this tells us that this interval is in our solution set.\r
\n" ); document.write( "\n" ); document.write( " So part our solution in interval notation is (

)

(

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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2-5x%2B1\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"2%28-4%29%5E2-5%28-4%29%2B1\"$ Plug in $\"x=-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2%2816%29-5%28-4%29%2B1\"$ Square $\"-4\"$ to get $\"16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"32-5%28-4%29%2B1\"$ Multiply $\"2\"$ and $\"16\"$ to get $\"32\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"32%2B20%2B1\"$ Multiply $\"-5\"$ and $\"-4\"$ to get $\"20\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"53\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2-5x%2B1=53\"$ when $\"x=-4\"$ \r
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\r
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\n" ); document.write( "\n" ); document.write( "# 4\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E8-3%29%28x%5E9-3%29\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( "Now let's FOIL the expression.\r
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\n" ); document.write( "\n" ); document.write( "Remember, when you FOIL an expression, you follow this procedure:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28highlight%289x%5E8%29-3%29%28highlight%28x%5E9%29-3%29\"$ Multiply the First terms: $\"%289%2Ax%5E8%29%2A%28x%5E9%29=9%2Ax%5E17\"$ . Note: simply add the exponents\r
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\n" ); document.write( "\n" ); document.write( " $\"%28highlight%289x%5E8%29-3%29%28x%5E9%2Bhighlight%28-3%29%29\"$ Multiply the Outer terms: $\"%289%2Ax%5E8%29%2A%28-3%29=-27%2Ax%5E8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E8%2Bhighlight%28-3%29%29%28highlight%28x%5E9%29-3%29\"$ Multiply the Inner terms: $\"%28-3%29%2A%28x%5E9%29=-3%2Ax%5E9\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%289x%5E8%2Bhighlight%28-3%29%29%28x%5E9%2Bhighlight%28-3%29%29\"$ Multiply the Last terms: $\"%28-3%29%2A%28-3%29=9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the terms: $\"9%2Ax%5E17\"$ , $\"-27%2Ax%5E8\"$ , $\"-3%2Ax%5E9\"$ , $\"9\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"9%2Ax%5E17-27%2Ax%5E8-3%2Ax%5E9%2B9\"$ Now add every term listed above to make a single expression.\r
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\n" ); document.write( "\n" ); document.write( "So $\"%289x%5E8-3%29%28x%5E9-3%29\"$ FOILs to $\"9%2Ax%5E17-27%2Ax%5E8-3%2Ax%5E9%2B9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"%289x%5E8-3%29%28x%5E9-3%29=9%2Ax%5E17-27%2Ax%5E8-3%2Ax%5E9%2B9\"$ .
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