document.write( "Question 283912: how do you solve g(x)= x^2+x+12 using the quadratic formula? \n" ); document.write( "

Algebra.Com's Answer #206064 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"g%28x%29=+x%5E2%2Bx%2B12\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"0=+x%5E2%2Bx%2B12\"$ Plug in $\"g%28x%29=0\"$ \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 $\"x%5E2%2Bx%2B12=0\"$ ( notice $\"a=1\"$ , $\"b=1\"$ , and $\"c=12\"$ )
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\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A12+%29%29%2F%282%2A1%29\"$ Plug in a=1, b=1, and c=12
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\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A12+%29%29%2F%282%2A1%29\"$ Square 1 to get 1
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\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+1%2B-48+%29%29%2F%282%2A1%29\"$ Multiply $\"-4%2A12%2A1\"$ to get $\"-48\"$
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\n" ); document.write( " $\"x+=+%28-1+%2B-+sqrt%28+-47+%29%29%2F%282%2A1%29\"$ Combine like terms in the radicand (everything under the square root)
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\n" ); document.write( " $\"x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%2A1%29\"$ 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( " $\"x+=+%28-1+%2B-+i%2Asqrt%2847%29%29%2F%282%29\"$ 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( " $\"x=-1%2F2%2Bsqrt%2847%29%2F2%2Ai\"$ or $\"x=-1%2F2-sqrt%2847%29%2F2%2Ai\"$
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\n" ); document.write( "\n" ); document.write( "Note: if you've never seen or heard of complex/imaginary numbers, then the answer is simply \"no solutions\". \n" ); document.write( "

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