Solve for $x$ :
$(x - 5)^{2} - (x + 2)^{2} = - 2$

x = 1 \frac{5}{4}

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x = 1 \frac{9}{14}

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x = 1 \frac{7}{17}

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x = 1 \frac{3}{13}

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Solution

The correct option is D $x = 1 \frac{9}{14}$
Given, $(x - 5)^{2} - (x + 2)^{2} = - 2$
$\Rightarrow x^{2} - 10 x + 25 - (x^{2} + 4 x + 4) = - 2$
$\Rightarrow x^{2} - 10 x + 25 - x^{2} - 4 x - 4 = - 2$
$\Rightarrow - 10 x - 4 x + 25 - 4 = - 2$
$\Rightarrow - 14 x = - 23$
$\Rightarrow x = \frac{23}{14} = 1 \frac{9}{14}$

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