SOLUTION: Solve for x: sqr(5x)-sqr(2x)=3

Algebra ->  Expressions -> SOLUTION: Solve for x: sqr(5x)-sqr(2x)=3      Log On


   



Question 1102591: Solve for x:
sqr(5x)-sqr(2x)=3

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(5x)-sqr(2x)=3, put one sqrt on each side
sqrt(5x)=3+sqrt (2x)
square both sides
5x=9+6 sqrt(2x)+2x
3x-9=6 sqrt (2x) divide everything by 3
x-3=2 sqrt (2x)
square both sides
(x-3)^2=4*2x=8x
expand
x^2-6x+9=8x
x^2-14x+9=0
x=(1/2)(14+/- sqrt (196-36); sqrt (160)=12.65
x=(1/2)(26.65)=13.33
x=(1/2)(1.35)=0.68
check both
sqrt(3.4)-sqrt(1.36) does not equal 3
sqrt (66.65)-sqrt(26.66)=3 ANSWER is x=13.33
graph%28300%2C300%2C-10%2C20%2C-10%2C10%2Cx%5E2-14x%2B9%2Csqrt%285x%29-sqrt%282x%29-3%29 the steep slope is the roots of x^2-14x+9, and the shallow slope is the original equation minus 3, and the value of x is the result. It equals 0 at 13.33