document.write( "Question 495770: I'm stuck on a question that I believe involves imaginary numbers. The problem is to solve $\"+%287x%2B6%29%5E2=-36+\"$ . I have re-written and FOIL'd the problem to be $\"+49x%5E2%2B84x%2B36=-36+\"$ and re-wrote it to $\"+49x%5E2%2B84x%2B72=0+\"$ . At this point, I'm am having trouble finding the possible factors in order to solve for 'x'. I know it has to involve 'i' since the original involves a negative. Any assistance will be greatly appreciated. Thank you! \n" ); document.write( "

Algebra.Com's Answer #336184 by kingme18(98) $\"\"$ $\"About$

You can put this solution on YOUR website!
You did a great job with the expansion, and your way will work if you use the quadratic formula ( $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ ) using a=49, b=84, and c=72.\r
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\n" ); document.write( "\n" ); document.write( "However, another approach to take is to use the fact that the polynomial is already written as a perfect square. If you take the square root of both sides, you'll have $\"+sqrt%28%287x%2B6%29%5E2%29=+%22%2B-%22+sqrt%28-36%29+\"$ , or $\"7x%2B6=%22%2B-%226i\"$ (sorry about the awkwardness with the positive/negatives...just remember that when you take the square root on both sides, you could get either a positive or negative). To solve, subtract 6 from both sides ( $\"7x=-6+%2B-+6i\"$ ) then divide everything by 7: $\"x=-6%2F7%2B-expr%286%2F7%29i\"$ ; broken up, you two answers are $\"x=-6%2F7%2Bexpr%286%2F7%29i\"$ and $\"x=-6%2F7-expr%286%2F7%29i\"$ \n" ); document.write( "

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