document.write( "Question 397233: Demonstrate how your quadratic equation is solved by the Quadratic Formula. Explain your steps.
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Algebra.Com's Answer #281577 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
Enter the coefficients of the quadratic in the form of $\"ax%5E2+%2B+bx+%2B+c=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+13=+4x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+-4x+%2B+13=+0\"$ \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 $\"x%5E2-4%2Ax%2B13=0\"$ ( notice $\"a=1\"$ , $\"b=-4\"$ , and $\"c=13\"$ )
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\n" ); document.write( " $\"x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29\"$ Plug in a=1, b=-4, and c=13
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\n" ); document.write( " $\"x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29\"$ Negate -4 to get 4
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\n" ); document.write( " $\"x+=+%284+%2B-+sqrt%28+16-4%2A1%2A13+%29%29%2F%282%2A1%29\"$ Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because $\"%28-4%29%5E2=-4%2A-4=16\"$ .)
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\n" ); document.write( " $\"x+=+%284+%2B-+sqrt%28+16%2B-52+%29%29%2F%282%2A1%29\"$ Multiply $\"-4%2A13%2A1\"$ to get $\"-52\"$
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\n" ); document.write( " $\"x+=+%284+%2B-+sqrt%28+-36+%29%29%2F%282%2A1%29\"$ Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " $\"x+=+%284+%2B-+6%2Ai%29%2F%282%2A1%29\"$ 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( " $\"x+=+%284+%2B-+6%2Ai%29%2F%282%29\"$ 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( " $\"x=2%2B3%2Ai\"$ or $\"x=2-3%2Ai\"$
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