SOLUTION: I'm stuck on a question that I believe involves imaginary numbers. The problem is to solve {{{ (7x+6)^2=-36 }}} . I have re-written and FOIL'd the problem to be {{{ 49x^2+84x+36=-3

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm stuck on a question that I believe involves imaginary numbers. The problem is to solve {{{ (7x+6)^2=-36 }}} . I have re-written and FOIL'd the problem to be {{{ 49x^2+84x+36=-3      Log On


   

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!
Answer by kingme18(98) About Me  (Show Source):
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.

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