SOLUTION: I need help with the follow Geometry word problem. The measure of the 1st angle is 7 times more than one third of the measure of the second angle squared. If the angles are supp

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Question 362979: I need help with the follow Geometry word problem.
The measure of the 1st angle is 7 times more than one third of the measure of the second angle squared. If the angles are supplementary find the measure of each angle.
My attempt: 7x + 1/3x^2 = 180
Thank you for your help.
Peter
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm a little confused.
Is it 7 more than 1/3 of the second angle squared or is it 7 times more than (1/3) of the second angle squared???
First name your variables.
Let the two angle be A and S.
By definition,
A%2BS=180
A=7%2B%281%2F3%29S%5E2
Substitute,
7%2B%281%2F3%29S%5E2%2BS=180
21%2BS%5E2%2B3S=540
S%5E2%2B3S-519=0
Use the quadratic formula,
S+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-519%29+%29%29%2F%282%2A1%29+
S+=+%28-3+%2B-+sqrt%28+9%2B2076+%29%29%2F%282%29+
S+=+%28-3+%2B-+sqrt%28+2085+%29%29%2F%282%29+
Only the positive solution makes sense here,
S+=+%28-3+%2B+sqrt%28+2085+%29%29%2F%282%29+
Then,
A%2B%28-3%2Bsqrt%282085%29%29%2F2=180
A=360%2F2-%28-3%2Bsqrt%282085%29%29%2F2
A=%28363-sqrt%282085%29%29%2F2
.
.
.
The other way,
A%2BS=180
A=7%281%2F3%29S%5E2
Substitute,
%287%2F3%29S%5E2%2BS=180
7S%5E2%2B3S=540
7S%5E2%2B3S-540=0
You can factor that one,
%287S-60%29%28S%2B9%29=0
Only the positive solution makes sense here,
7S-60=0
7S=60
S=60%2F7
Then
A=180-60%2F7
A=1260%2F7-60%2F7
A=1200%2F7