Question

Solve the following equations for $x$.
${(x-5)}^2=4{(x+5)}^2$

• A. $-15$
• B. $\frac{-1}{5}$
• C. $\frac{-5}{3}$
• D. $-5$

Answer 1

Answer: (A), (C)

$-15$
$\frac{-5}{3}$

Given, ${(x-5)}^2=4{(x+5)}^2$
$\Rightarrow x^2-10x+25$ $=4x^2+40x+100$

$\Rightarrow 3x^2+50x+75=0$

The roots of the equation are $x=\frac{(-50\pm \sqrt{2500-900})}{6}$

$=\frac{(-50\pm \sqrt{1600})}{6}$

$=\frac{(-50\pm 40)}{6}$

$=-15,-\frac{5}{3}$