SOLUTION: Please help me solve this. {{{sqrt(10x-4)+sqrt(16x+17)=sqrt(75x-29)}}} I also need to know all the steps and why it works. Thanks you very much for your time.

Algebra ->  Radicals -> SOLUTION: Please help me solve this. {{{sqrt(10x-4)+sqrt(16x+17)=sqrt(75x-29)}}} I also need to know all the steps and why it works. Thanks you very much for your time.      Log On


   

Question 604223: Please help me solve this.
sqrt%2810x-4%29%2Bsqrt%2816x%2B17%29=sqrt%2875x-29%29
I also need to know all the steps and why it works.
Thanks you very much for your time.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2810x-4%29%2Bsqrt%2816x%2B17%29=sqrt%2875x-29%29


Square both sides

10x-4+%2B2sqrt%2810x-4%29%2Asqrt%2816x%2B17%29%2B16x%2B17+=+75x-29

26x%2B13+%2B2sqrt%2810x-4%29%2Asqrt%2816x%2B17%29=+75x-29

2sqrt%2810x-4%29%2Asqrt%2816x%2B17%29=+49x-42
square both sides
4%2810x-4%29%2816x%2B17%29=%2849x-42%29%5E2

4%28160x%5E2%2B170x-64x-78%29=%2849x-42%29%5E2

4%28160x%5E2%2B106x-78%29=2401x%5E2-4116x%2B1764

640x%5E2%2B424x-312=2401x%5E2-4116x%2B1764
1761x%5E2-4540x%2B2076=0
Find the roots of the equation by quadratic formula

a= 1761 , b= -4540 , c= 2076

b^2-4ac= 20611600 -14623344
b^2-4ac= 5988256
%09sqrt%28%095988256%09%29=%092447.09%09
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 4540 + 2447.09 )/ 3522
x1= 1.98
x2=%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x2=( 4540 -2447.09 ) / 3522
x2= 0.59

(1.98,0.59)