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Simplifying (x + 5)(x + 5) = 65 + x(x + 2) Reorder the terms: (5 + x)(x + 5) = 65 + x(x + 2) Reorder the terms: (5 + x)(5 + x) = 65 + x(x + 2) Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 65 + x(x + 2) ((5 * 5 + x * 5) + x(5 + x)) = 65 + x(x + 2) ((25 + 5x) + x(5 + x)) = 65 + x(x + 2) (25 + 5x + (5 * x + x * x)) = 65 + x(x + 2) (25 + 5x + (5x + x2)) = 65 + x(x + 2) Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 65 + x(x + 2) Reorder the terms: 25 + 10x + x2 = 65 + x(2 + x) 25 + 10x + x2 = 65 + (2 * x + x * x) 25 + 10x + x2 = 65 + (2x + x2) Add '-1x2' to each side of the equation. 25 + 10x + x2 + -1x2 = 65 + 2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 10x + 0 = 65 + 2x + x2 + -1x2 25 + 10x = 65 + 2x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 10x = 65 + 2x + 0 25 + 10x = 65 + 2x Solving 25 + 10x = 65 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. 25 + 10x + -2x = 65 + 2x + -2x Combine like terms: 10x + -2x = 8x 25 + 8x = 65 + 2x + -2x Combine like terms: 2x + -2x = 0 25 + 8x = 65 + 0 25 + 8x = 65 Add '-25' to each side of the equation. 25 + -25 + 8x = 65 + -25 Combine like terms: 25 + -25 = 0 0 + 8x = 65 + -25 8x = 65 + -25 Combine like terms: 65 + -25 = 40 8x = 40 Divide each side by '8'. x = 5 Simplifying x = 5
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