Expert: Azeem Hussain - 9/18/2009

Question
Hello Azeem,

My daughter posed this question to me, and I can't seem to solve it: Angle A and Angle B are complementary.  Angle A has a value of -2x2 (negative 2x squared) + 10; Angle B has a value of 8x + 16.  What is the value of x and what are the associated angles?

I tried the standard solution -2x2 + 10 + 8x + 16 = 90 and resolved it to -2x2 + 8x = 64; then further to x2 - 4x + 32 = 0, but from there I’m stuck, since the +32 value cannot be factored to result in a negative 4 in the - 4x term.

Can you help? Could the -2x2 be a typo and if it is, how to solve for a value of 2x2?  I'm stumped!

Thanks and regards,
Mike Majlak

Answer
Hi Mike!

As written, there is no solution to the quadratic equation.

Assuming there is a typo and it's supposed to be positive 2x², the equation becomes
2x²+8x-64=0
x²+4x-32=0

Which can be factored as
(x+8)(x-4)=0

Therefore x=-8, and x=4.

<B=8x+16
<B=8(-8)+16
<B=-48

Uh oh!  Both angles must measure between 0 and 90 degrees, so -48 degrees is nonsensical.  Therefore, x may not equal -8 in this problem.  It must equal 4.  Substituting x into the initial expressions for the angles measures, <A=42° and <B=48°.

Thanks for asking,
Azeem