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Simplifying (x + 5)(x + 5) + k(x + 5) + 30 = 0 Reorder the terms: (5 + x)(x + 5) + k(x + 5) + 30 = 0 Reorder the terms: (5 + x)(5 + x) + k(x + 5) + 30 = 0 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) + k(x + 5) + 30 = 0 ((5 * 5 + x * 5) + x(5 + x)) + k(x + 5) + 30 = 0 ((25 + 5x) + x(5 + x)) + k(x + 5) + 30 = 0 (25 + 5x + (5 * x + x * x)) + k(x + 5) + 30 = 0 (25 + 5x + (5x + x2)) + k(x + 5) + 30 = 0 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) + k(x + 5) + 30 = 0 Reorder the terms: 25 + 10x + x2 + k(5 + x) + 30 = 0 25 + 10x + x2 + (5 * k + x * k) + 30 = 0 25 + 10x + x2 + (5k + kx) + 30 = 0 Reorder the terms: 25 + 30 + 5k + kx + 10x + x2 = 0 Combine like terms: 25 + 30 = 55 55 + 5k + kx + 10x + x2 = 0 Solving 55 + 5k + kx + 10x + x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + 5k + kx + 10x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + 5k + kx + 10x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + 5k + kx + 10x + x2 = 0 + -55 5k + kx + 10x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 5k + kx + 10x + x2 = -55 Add '-10x' to each side of the equation. 5k + kx + 10x + -10x + x2 = -55 + -10x Combine like terms: 10x + -10x = 0 5k + kx + 0 + x2 = -55 + -10x 5k + kx + x2 = -55 + -10x Add '-1x2' to each side of the equation. 5k + kx + x2 + -1x2 = -55 + -10x + -1x2 Combine like terms: x2 + -1x2 = 0 5k + kx + 0 = -55 + -10x + -1x2 5k + kx = -55 + -10x + -1x2 Reorder the terms: 55 + 5k + kx + 10x + x2 = -55 + -10x + -1x2 + 55 + 10x + x2 Reorder the terms: 55 + 5k + kx + 10x + x2 = -55 + 55 + -10x + 10x + -1x2 + x2 Combine like terms: -55 + 55 = 0 55 + 5k + kx + 10x + x2 = 0 + -10x + 10x + -1x2 + x2 55 + 5k + kx + 10x + x2 = -10x + 10x + -1x2 + x2 Combine like terms: -10x + 10x = 0 55 + 5k + kx + 10x + x2 = 0 + -1x2 + x2 55 + 5k + kx + 10x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 55 + 5k + kx + 10x + x2 = 0 The solution to this equation could not be determined.
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