document.write( "Question 157986: 24. Find b^2 – 4ac and the number of real solutions for the given equation.
\n" ); document.write( "–x^2 + 12x – 32 = 0 \n" ); document.write( "

Algebra.Com's Answer #116391 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "From $\"-x%5E2%2B12x-32\"$ we can see that $\"a=-1\"$ , $\"b=12\"$ , and $\"c=-32\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=b%5E2-4ac\"$ Start with the discriminant formula.\r
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\n" ); document.write( "\n" ); document.write( " $\"D=%2812%29%5E2-4%28-1%29%28-32%29\"$ Plug in $\"a=-1\"$ , $\"b=12\"$ , and $\"c=-32\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=144-4%28-1%29%28-32%29\"$ Square $\"12\"$ to get $\"144\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=144-128\"$ Multiply $\"4%28-1%29%28-32%29\"$ to get $\"%28-4%29%28-32%29=128\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"D=16\"$ Subtract $\"128\"$ from $\"144\"$ to get $\"16\"$ \r
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\n" ); document.write( "\n" ); document.write( "Since the discriminant is greater than zero, this means that there are two real solutions.
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