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

Question 1102591: Solve for x:
sqr(5x)-sqr(2x)=3
Answer by Boreal(15235) (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
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
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