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(A) Given equation: $x^{2} + (x + 5)^{2} = 625$Expand the square: $x^{2} + (x^{2} + 10x + 25) = 625$Combine like terms: $2x^{2} + 10x + 25 = 625$Subtr

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$15, -20$

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(A) Given equation: $x^{2} + (x + 5)^{2} = 625$Expand the square: $x^{2} + (x^{2} + 10x + 25) = 625$Combine like terms: $2x^{2} + 10x + 25 = 625$Subtract $625$ from both sides: $2x^{2} + 10x - 600 = 0$Divide the entire equation by $2$: $x^{2} + 5x - 300 = 0$Factorize the quadratic equation by splitting the middle term: $x^{2} + 20x - 15x - 300 = 0$Group the terms: $x(x + 20) - 15(x + 20) = 0$Factor out $(x + 20)$: $(x + 20)(x - 15) = 0$Set each factor to zero: $x + 20 = 0$ or $x - 15 = 0$Therefore,the solutions are $x = -20$ and $x = 15$.

Solve the following equation using the method of factorization: $x^{2} + (x + 5)^{2} = 625$

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