Solving radical equation

[leonardwl]

Hi. The equation is x - 4*(square root)x = 32. First, I thought on turning it into a quadratic by squaring both sides, but would still leave the square root of X in the equation. Thanks for any help.

 

[pka]

Hi. The equation is x - 4*(square root)x = 32. First, I thought on turning it into a quadratic by squaring both sides, but would still leave the square root of X in the equation. Thanks for any help.

If \(\displaystyle y=\sqrt{x}\) you problem becomes
\(\displaystyle \\y^2-4y-32=0\\(y+4)(y-8)=0\\y=-4\text{ or }y=8\)

But \(\displaystyle y=\sqrt{x}\ne -4\) so \(\displaystyle y=\sqrt{x}=8\).

What is the solution?