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Simplifying x(x + 5) + 1 = (x + 6)(x + 6) Reorder the terms: x(5 + x) + 1 = (x + 6)(x + 6) (5 * x + x * x) + 1 = (x + 6)(x + 6) (5x + x2) + 1 = (x + 6)(x + 6) Reorder the terms: 1 + 5x + x2 = (x + 6)(x + 6) Reorder the terms: 1 + 5x + x2 = (6 + x)(x + 6) Reorder the terms: 1 + 5x + x2 = (6 + x)(6 + x) Multiply (6 + x) * (6 + x) 1 + 5x + x2 = (6(6 + x) + x(6 + x)) 1 + 5x + x2 = ((6 * 6 + x * 6) + x(6 + x)) 1 + 5x + x2 = ((36 + 6x) + x(6 + x)) 1 + 5x + x2 = (36 + 6x + (6 * x + x * x)) 1 + 5x + x2 = (36 + 6x + (6x + x2)) Combine like terms: 6x + 6x = 12x 1 + 5x + x2 = (36 + 12x + x2) Add '-1x2' to each side of the equation. 1 + 5x + x2 + -1x2 = 36 + 12x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + 5x + 0 = 36 + 12x + x2 + -1x2 1 + 5x = 36 + 12x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + 5x = 36 + 12x + 0 1 + 5x = 36 + 12x Solving 1 + 5x = 36 + 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. 1 + 5x + -12x = 36 + 12x + -12x Combine like terms: 5x + -12x = -7x 1 + -7x = 36 + 12x + -12x Combine like terms: 12x + -12x = 0 1 + -7x = 36 + 0 1 + -7x = 36 Add '-1' to each side of the equation. 1 + -1 + -7x = 36 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 36 + -1 -7x = 36 + -1 Combine like terms: 36 + -1 = 35 -7x = 35 Divide each side by '-7'. x = -5 Simplifying x = -5
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