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

- 15

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\frac{- 1}{5}

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\frac{- 5}{3}

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- 5

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Solution

The correct options are
A $- 15$
B $\frac{- 5}{3}$
Given, ${(x - 5)}^{2} = 4 {(x + 5)}^{2}$
$\Rightarrow x^{2} - 10 x + 25$ $= 4 x^{2} + 40 x + 100$
$\Rightarrow 3 x^{2} + 50 x + 75 = 0$
The roots of the equation are $x = \frac{(- 50 \pm \sqrt{2500 - 900})}{6}$
$= \frac{(- 50 \pm \sqrt{1600})}{6}$
$= \frac{(- 50 \pm 40)}{6}$
$= - 15, - \frac{5}{3}$

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