document.write( "Question 107217: i have worked this problem several times and I havent been able to come close to solving it.\r
\n" ); document.write( "\n" ); document.write( "8x^2=30x+8 the ^2 means to the 2nd power. I wasn't sure how to enter exponents. Can anyone help me?
\n" ); document.write( " Thank you, \n" ); document.write( "
Algebra.Com's Answer #78040 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Given:
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\n" ); document.write( "\"8x%5E2+=+30x%2B8+\"
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\n" ); document.write( "To solve for x you can begin by changing the arrangement of the given equation. You want to
\n" ); document.write( "have all the terms on the left side of the equation and have the right side equal to zero.
\n" ); document.write( "This is a \"standard\" arrangement for a quadratic equation. Therefore you can get rid of the
\n" ); document.write( "two terms on the right side as follows. First subtract 30x from both sides of this equation.
\n" ); document.write( "On the right side subtracting 30x cancels out the 30x. And the subtraction of 30x from the left
\n" ); document.write( "side makes the equation become:
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\n" ); document.write( "\"8x%5E2+-+30x+=+8\"
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\n" ); document.write( "Next, following the same type of process, get rid of the 8 on the right side by subtracting
\n" ); document.write( "8 from both sides. When you do that the equation is converted to the standard quadratic form:
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\n" ); document.write( "\"8x%5E2+-+30x+-+8+=+0\"
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\n" ); document.write( "Notice that you can simplify this a little bit by dividing both sides (all terms) by 2
\n" ); document.write( "because 2 is a factor common to all the numbers of this equation. This division leads the
\n" ); document.write( "equation to become:
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\n" ); document.write( "\"4x%5E2+-+15x+-+4+=+0\"
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\n" ); document.write( "Now you can apply the quadratic formula. The quadratic formula says that if you have a quadratic
\n" ); document.write( "equation in the standard form of:
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\n" ); document.write( "\"ax%5E2+%2B+bx+%2B+c+=+0\"
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\n" ); document.write( "then the solutions for x are given by the equation:
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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( "Well, your equation is certainly in the standard form. Compare like terms of the standard
\n" ); document.write( "form with your equation and you will see that:
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\n" ); document.write( "\"ax%5E2+=+4x%5E2\" will be the same if a = 4
\n" ); document.write( "\"bx+=+-15x\" will be the same if b = -15 and
\n" ); document.write( "\"c+=+-4\" identifies c
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\n" ); document.write( "So you now know the values for a, b, and c. To solve for x you just substitute these values
\n" ); document.write( "into the equation for x above. Substituting these values results in:
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\n" ); document.write( "Note that -(-15) is +15. Also note that \"%28-15%29%5E2\" is +225. And -4*4*-4 is +64. And
\n" ); document.write( "finally in the denominator, 2*4 = 8. Substitute these values into the equation for x and
\n" ); document.write( "you get:
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\n" ); document.write( "\"x+=+%2815+%2B-+sqrt%28225%2B64%29%29%2F8+=+%2815%2B-sqrt%28289%29%29%2F8\"
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\n" ); document.write( "The square root of 289 is 17, and when this is substituted the equation for x becomes:
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\n" ); document.write( "\"x+=+%2815+%2B-+17%29%2F8\"
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\n" ); document.write( "First use the plus sign in the numerator and you get:
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\n" ); document.write( "\"x+=+%2815%2B17%29%2F8+=+32%2F8+=+4\"
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\n" ); document.write( "Then use the minus sign in the numerator\"
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\n" ); document.write( "\"x+=+%2815-17%29%2F8+=+-2%2F8+=+-1%2F4\"
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\n" ); document.write( "So the two answers to this problem are x = 4 and x = -1/4
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\n" ); document.write( "You can validate these answers by substituting them for x in the original problem and
\n" ); document.write( "showing that both sides of that equation remain equal.
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\n" ); document.write( "As an example, the original problem is:
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\n" ); document.write( "\"8x%5E2+=+30x%2B8+\"
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\n" ); document.write( "If you set x equal to 4 this equation becomes:
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\n" ); document.write( "\"8%2A%284%5E2%29+=+30%284%29+%2B+8\"
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\n" ); document.write( "The \"4%5E2+=+16\" and \"30%2A4+=+120\"
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\n" ); document.write( "Substituting these results in:
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\n" ); document.write( "\"8%2A16+=+120+%2B+8\"
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\n" ); document.write( "On the left side the 8*16 = 128 and on the right side the 120 + 8 = 128. So the equation
\n" ); document.write( "is 128 = 128 which shows that the equation is true when x = 4. Therefore, x = 4 is a
\n" ); document.write( "good answer.
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\n" ); document.write( "You can do the same sort of check by letting x = -1/4 in the original equation and again
\n" ); document.write( "showing that the left side of the equation equals the right side of the equation.
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\n" ); document.write( "Hope this helps you to understand the problem and how you can get the two answers for x.
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