Question

(x-5)^2 -(x+2)^2 = -2

Answer 1

Answer:

Given ,

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

after expanding

${x}^{2} + 25 - 10x - ( {x}^{2} + 4 + 4x) = - 2$

${x}^{2} + 25 - 10x - {x}^{2} - 4 - 4x + 2 = 0$

$21 - 14x + 2 = 0 \\ 23 - 14x = 0$

$14x = 23 \\ x = \frac{23}{14}$

Answer 2

Step-by-step explanation:

$\sf{(x-5)^{2}-(x+2)^{2}=-2}$

$\implies{\sf{(x^{2}-10x+25)-(x^{2}+4x+4)=-2}}$

$\implies{\sf{x^{2}-10x+25-x^{2}-4x-4=-2}}$

$\implies{\sf{-14x+21=-2}}$

$\implies{\sf{-14x=-2-21}}$.

$\implies{\sf{x=\frac{-23}{-14}}}$

$\implies{\boxed{\sf{x=\frac{23}{14}}}}$

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