document.write( "Question 597807: Solve : $\"-5x%5E2%2B5=-2x+\"$ \n" ); document.write( "

Algebra.Com's Answer #378348 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"-5x%5E2%2B5=-2x+\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"-5x%5E2%2B5%2B2x+=+0+\"$ Add 2x to both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"-5x%5E2%2B2x%2B5+=+0+\"$ Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%5E2-2x-5+=+0+\"$ Multiply every term by -1 to make the leading coefficient positive.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic $\"5x%5E2-2x-5\"$ is in the form of $\"Ax%5E2%2BBx%2BC\"$ where $\"A=5\"$ , $\"B=-2\"$ , and $\"C=-5\"$ \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( " $\"x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%285%29%28-5%29+%29%29%2F%282%285%29%29\"$ Plug in $\"A=5\"$ , $\"B=-2\"$ , and $\"C=-5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%285%29%28-5%29+%29%29%2F%282%285%29%29\"$ Negate $\"-2\"$ to get $\"2\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+4-4%285%29%28-5%29+%29%29%2F%282%285%29%29\"$ Square $\"-2\"$ to get $\"4\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+4--100+%29%29%2F%282%285%29%29\"$ Multiply $\"4%285%29%28-5%29\"$ to get $\"-100\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+4%2B100+%29%29%2F%282%285%29%29\"$ Rewrite $\"sqrt%284--100%29\"$ as $\"sqrt%284%2B100%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+104+%29%29%2F%282%285%29%29\"$ Add $\"4\"$ to $\"100\"$ to get $\"104\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+sqrt%28+104+%29%29%2F%2810%29\"$ Multiply $\"2\"$ and $\"5\"$ to get $\"10\"$ . \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282+%2B-+2%2Asqrt%2826%29%29%2F%2810%29\"$ Simplify the square root (note: If you need help with simplifying square roots, check out this solver) \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%282%2B2%2Asqrt%2826%29%29%2F%2810%29\"$ or $\"x+=+%282-2%2Asqrt%2826%29%29%2F%2810%29\"$ Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( " $\"x+=+%281%2Bsqrt%2826%29%29%2F%285%29\"$ or $\"x+=+%281-sqrt%2826%29%29%2F%285%29\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are $\"x+=+%281%2Bsqrt%2826%29%29%2F%285%29\"$ or $\"x+=+%281-sqrt%2826%29%29%2F%285%29\"$
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