SOLUTION: I don't have a book. This is a summer assignment. Solve the following eqation {{{ x^2 + 10x - 16 = 0 }}}

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Question 150983: I don't have a book. This is a summer assignment.
Solve the following eqation +x%5E2+%2B+10x+-+16+=+0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B10x-16=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=10, and c=-16


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%2810%29+%2B-+sqrt%28+%2810%29%5E2-4%281%29%28-16%29+%29%29%2F%282%281%29%29 Plug in a=1, b=10, and c=-16


x+=+%28-10+%2B-+sqrt%28+100-4%281%29%28-16%29+%29%29%2F%282%281%29%29 Square 10 to get 100.


x+=+%28-10+%2B-+sqrt%28+100--64+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-16%29 to get -64


x+=+%28-10+%2B-+sqrt%28+100%2B64+%29%29%2F%282%281%29%29 Rewrite sqrt%28100--64%29 as sqrt%28100%2B64%29


x+=+%28-10+%2B-+sqrt%28+164+%29%29%2F%282%281%29%29 Add 100 to 64 to get 164


x+=+%28-10+%2B-+sqrt%28+164+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-10+%2B-+2%2Asqrt%2841%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-10%29%2F%282%29+%2B-+%282%2Asqrt%2841%29%29%2F%282%29 Break up the fraction.


x+=+-5+%2B-+sqrt%2841%29 Reduce.


x+=+-5%2Bsqrt%2841%29 or x+=+-5-sqrt%2841%29 Break up the expression.


So our answers are x+=+-5%2Bsqrt%2841%29 or x+=+-5-sqrt%2841%29


which approximate to x=1.403 or x=-11.403