document.write( "Question 111423: I am having trouble with all five of these quadratic equations PLEASE HELP!
\n" ); document.write( "1. \"+9%28x-8%29%5E2+=+36+\"
\n" ); document.write( "2. \"+27x%5E2+-+49+=+0+\"
\n" ); document.write( "3. \"+-16x+=+-x%5E2+\"
\n" ); document.write( "4. \"+x%5E3+-4x%5E2+%2B+4X+=+0+\"
\n" ); document.write( "5. \"+x%5E2+%2B+69+=+0+\"\r
\n" ); document.write( "\n" ); document.write( "Any help would be greatly appreciated. I am going to continue working on these problems. They are due today by 4:30 p.m. est.
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Algebra.Com's Answer #81254 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( " Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-8%29%5E2=4\" Divide both sides by 9\r
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\n" ); document.write( "\n" ); document.write( " Take the square root of both sides\r
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\n" ); document.write( "\n" ); document.write( " Simplify the square root (note: If you need help with simplifying the square root, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( " Add 8 to both sides to isolate x.\r
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\n" ); document.write( "\n" ); document.write( " Break down the expression into two parts:\r
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document.write( "   or  \r\n" );
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\n" ); document.write( "\n" ); document.write( " Now combine like terms for each expression:\r
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document.write( "   or      
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\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "\n" ); document.write( "So our solution is\r
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document.write( "  or   \r\n" );
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\n" ); document.write( "\n" ); document.write( " Notice when we graph the equations \"y=9%28x-8%29%5E2\" and \"y=36\" we get:\r
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\n" ); document.write( "\n" ); document.write( " graph of \"y=9%28x-8%29%5E2\" (red) and \"y=36\" (green)\r
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\n" ); document.write( "\n" ); document.write( "Here we can see that the two equations intersect at x values of \"x=10\" and \"x=6\", so this verifies our answer.\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"27%2Ax%5E2-49=0\" (note: since the polynomial does not have an \"x\" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like \"27%2Ax%5E2%2B0%2Ax-49=0\" notice \"a=27\", \"b=0\", and \"c=-49\")
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A27%2A-49+%29%29%2F%282%2A27%29\" Plug in a=27, b=0, and c=-49
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+0-4%2A27%2A-49+%29%29%2F%282%2A27%29\" Square 0 to get 0
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+0%2B5292+%29%29%2F%282%2A27%29\" Multiply \"-4%2A-49%2A27\" to get \"5292\"
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+5292+%29%29%2F%282%2A27%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%280+%2B-+42%2Asqrt%283%29%29%2F%282%2A27%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%280+%2B-+42%2Asqrt%283%29%29%2F54\" Multiply 2 and 27 to get 54
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\n" ); document.write( " So now the expression breaks down into two parts
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\n" ); document.write( " \"x+=+%280+%2B+42%2Asqrt%283%29%29%2F54\" or \"x+=+%280+-+42%2Asqrt%283%29%29%2F54\"
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\n" ); document.write( " Now break up the fraction
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\n" ); document.write( " \"x=0%2F54%2B42%2Asqrt%283%29%2F54\" or \"x=0%2F54-42%2Asqrt%283%29%2F54\"
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\n" ); document.write( " Simplify
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\n" ); document.write( " \"x=0%2B7%2Asqrt%283%29%2F9\" or \"x=0-7%2Asqrt%283%29%2F9\"
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\n" ); document.write( " So the solutions are:
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\n" ); document.write( " \"x=0%2B7%2Asqrt%283%29%2F9\" or \"x=0-7%2Asqrt%283%29%2F9\"
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\n" ); document.write( "\n" ); document.write( " \"+-16x+=+-x%5E2+\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " \"+x%5E2-16x+=0++\"Add \"x%5E2\" to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"x%28x-16%29=0\" Factor the left side (note: if you need help with factoring, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( "\"x=0\" or \"x-16=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=0\" or \"x=16\" Now solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "So our solutions are \"x=0\" or \"x=16\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph \"y=x%5E2-16x\" we get\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28500%2C500%2C-20%2C20%2C-10%2C10%2C+x%5E2-16x%29+\"\r
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\n" ); document.write( "\n" ); document.write( "and we can see that the graph has roots at \"x=0\" or \"x=16\", so this verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E3-4x%5E2%2B4x=0\" Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( "\"x%28x%5E2-4x%2B4%29=0\" Factor out the GCF \"x\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%28x-2%29%28x-2%29=0\" Factor the inner expression \"x%5E2-4x%2B4\"\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( "\"x=0\", \"x-2=0\" or \"x-2=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"x=0\", \"x=2\", or \"x=2\" Now solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "Notice we get the solution \"x=2\" twice\r
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\n" ); document.write( "\n" ); document.write( "So our solutions are \"x=0\" or \"x=2\"\r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph \"y=x%5E3-4x%5E2%2B4x\" we get\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+x%5E3-4x%5E2%2B4x%29+\"\r
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\n" ); document.write( "\n" ); document.write( "and we can see that the graph has roots at \"x=0\" and \"x=2\" so this verifies our answer.\r
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Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:

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\n" ); document.write( " Starting with the general quadratic
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\n" ); document.write( " \"ax%5E2%2Bbx%2Bc=0\"
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\n" ); document.write( " the general solution using the quadratic equation is:
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\n" ); document.write( " \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"
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\n" ); document.write( " So lets solve \"x%5E2%2B69=0\" (note: since the polynomial does not have an \"x\" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like \"x%5E2%2B0%2Ax%2B69=0\" notice \"a=1\", \"b=0\", and \"c=69\")
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A69+%29%29%2F%282%2A1%29\" Plug in a=1, b=0, and c=69
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+0-4%2A1%2A69+%29%29%2F%282%2A1%29\" Square 0 to get 0
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+0%2B-276+%29%29%2F%282%2A1%29\" Multiply \"-4%2A69%2A1\" to get \"-276\"
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\n" ); document.write( " \"x+=+%280+%2B-+sqrt%28+-276+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " \"x+=+%280+%2B-+2%2Ai%2Asqrt%2869%29%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
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\n" ); document.write( " \"x+=+%280+%2B-+2%2Ai%2Asqrt%2869%29%29%2F%282%29\" Multiply 2 and 1 to get 2
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\n" ); document.write( " After simplifying, the quadratic has roots of
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\n" ); document.write( " \"x=0%2Bsqrt%2869%29i\" or \"x=0-sqrt%2869%29i\"
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