Math Is Fun Forum

Italo an der Kanti

Member

Registered: 2008-02-25

Posts: 1

Square Root Equation

Hey everyone! I'm doing some self teaching in math with a book that only shows answers but not how you get to the answers. Please help me with this equation, I just can't figure it out:

√(4x+9) - 2 = √(3x-5)              The answers are 10 and 18

I tried bringing the square roots on one side and squaring the whole thing but I come to -10, which is false. How does this work?

Thank you in advance,
Giovanni

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Square Root Equation

√(4x+9) - 2 = √(3x-5)
4x+9+4-4√(4x+9) = 3x-5   -> square both sides
x+18 = 4√(4x+9)  -> move square root to right side
x^2 + 36x + 324 = 64x + 144 -> square both sides again
x^2 - 28x + 180 = 0 -> collect terms into quadratic equation
(x-14)^2 = 16 -> completing the square
x - 14 = ±4
x = 14±4 = {10,18}

Last edited by luca-deltodesco (2008-02-25 04:56:08)

---

The Beginning Of All Things To End.
The End Of All Things To Come.