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Simplifying (x + 5)(x + 5) = (x + 4)(x + 4) Reorder the terms: (5 + x)(x + 5) = (x + 4)(x + 4) Reorder the terms: (5 + x)(5 + x) = (x + 4)(x + 4) Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = (x + 4)(x + 4) ((5 * 5 + x * 5) + x(5 + x)) = (x + 4)(x + 4) ((25 + 5x) + x(5 + x)) = (x + 4)(x + 4) (25 + 5x + (5 * x + x * x)) = (x + 4)(x + 4) (25 + 5x + (5x + x2)) = (x + 4)(x + 4) Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = (x + 4)(x + 4) Reorder the terms: 25 + 10x + x2 = (4 + x)(x + 4) Reorder the terms: 25 + 10x + x2 = (4 + x)(4 + x) Multiply (4 + x) * (4 + x) 25 + 10x + x2 = (4(4 + x) + x(4 + x)) 25 + 10x + x2 = ((4 * 4 + x * 4) + x(4 + x)) 25 + 10x + x2 = ((16 + 4x) + x(4 + x)) 25 + 10x + x2 = (16 + 4x + (4 * x + x * x)) 25 + 10x + x2 = (16 + 4x + (4x + x2)) Combine like terms: 4x + 4x = 8x 25 + 10x + x2 = (16 + 8x + x2) Add '-1x2' to each side of the equation. 25 + 10x + x2 + -1x2 = 16 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 10x + 0 = 16 + 8x + x2 + -1x2 25 + 10x = 16 + 8x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 10x = 16 + 8x + 0 25 + 10x = 16 + 8x Solving 25 + 10x = 16 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 25 + 10x + -8x = 16 + 8x + -8x Combine like terms: 10x + -8x = 2x 25 + 2x = 16 + 8x + -8x Combine like terms: 8x + -8x = 0 25 + 2x = 16 + 0 25 + 2x = 16 Add '-25' to each side of the equation. 25 + -25 + 2x = 16 + -25 Combine like terms: 25 + -25 = 0 0 + 2x = 16 + -25 2x = 16 + -25 Combine like terms: 16 + -25 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5
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