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Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve the fol...

Question

Solve the following equation :

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

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Solution

$(x - 5)^{2} - (x + 2)^{2} = - 2 \Rightarrow (x^{2} - 10 x + 25) - (x^{2} + 4 x + 4) = - 2 \Rightarrow x^{2} - 10 x + 25 - x^{2} - 4 x - 4 = - 2 \Rightarrow - 10 x - 4 x + 25 - 4 = - 2 \Rightarrow - 14 x = 4 - 2 - 25 = - 23 \Rightarrow x = \frac{- 23}{- 14} = \frac{23}{14} = 1 \frac{9}{14}$

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