SOLUTION: (5+sqrtx)^2-12(5+sqrtx)+33=0 solve

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: (5+sqrtx)^2-12(5+sqrtx)+33=0 solve      Log On


   

Question 323992: (5+sqrtx)^2-12(5+sqrtx)+33=0 solve
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute, let u=5%2Bsqrt%28x%29
u%5E2-12u%2B33=0
Use the quadratic formula,
u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
u+=+%2812+%2B-+sqrt%28+12%5E2-4%2A1%2A%2833%29+%29%29%2F%282%2A1%29+
u+=+%2812+%2B-+sqrt%28+144-132+%29%29%2F2+
u+=+%2812+%2B-+sqrt%28+12+%29%29%2F2+
u+=+%2812+%2B-+2sqrt%28+3+%29%29%2F2+
u+=+6+%2B-+sqrt%28+3+%29+
.
.
.
5%2Bsqrt%28x%29=6+%2B-+sqrt%283%29
.
.
.
5%2Bsqrt%28x%29=6%2Bsqrt%283%29
sqrt%28x%29=1%2Bsqrt%283%29
x=%281%2Bsqrt%283%29%29%5E2
x=1%2B2sqrt%283%29%2B3
highlight%28x=4%2B2sqrt%283%29%29 or approximately,
x=7.73
.
.
.
5%2Bsqrt%28x%29=6+-+sqrt%283%29
sqrt%28x%29=1-sqrt%283%29
sqrt%28x%29%3C0
No solution.
.
.
.