SOLUTION: One of two complementary angles is 120 less than the square of the othe. Find the measure of the bigger angle

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Question 1050160: One of two complementary angles is 120 less than the square of the othe. Find the measure of the bigger angle
Found 2 solutions by advanced_Learner, MathTherapy:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
x%2By=90

y=x%5E2-120
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-210+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-210=841.

Discriminant d=841 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+841+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+841+%29%29%2F2%5C1+=+14
x%5B2%5D+=+%28-%281%29-sqrt%28+841+%29%29%2F2%5C1+=+-15

Quadratic expression 1x%5E2%2B1x%2B-210 can be factored:
1x%5E2%2B1x%2B-210+=+1%28x-14%29%2A%28x--15%29
Again, the answer is: 14, -15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-210+%29

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

One of two complementary angles is 120 less than the square of the othe. Find the measure of the bigger angle
highlight_green%28matrix%281%2C3%2C+Larger%2C+%22angle%3A%22%2C+76%5Eo%29%29