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Simplifying (x + 5)(x + 1) = x2 + kx + 5 Reorder the terms: (5 + x)(x + 1) = x2 + kx + 5 Reorder the terms: (5 + x)(1 + x) = x2 + kx + 5 Multiply (5 + x) * (1 + x) (5(1 + x) + x(1 + x)) = x2 + kx + 5 ((1 * 5 + x * 5) + x(1 + x)) = x2 + kx + 5 ((5 + 5x) + x(1 + x)) = x2 + kx + 5 (5 + 5x + (1 * x + x * x)) = x2 + kx + 5 (5 + 5x + (1x + x2)) = x2 + kx + 5 Combine like terms: 5x + 1x = 6x (5 + 6x + x2) = x2 + kx + 5 Reorder the terms: 5 + 6x + x2 = 5 + kx + x2 Add '-5' to each side of the equation. 5 + 6x + -5 + x2 = 5 + kx + -5 + x2 Reorder the terms: 5 + -5 + 6x + x2 = 5 + kx + -5 + x2 Combine like terms: 5 + -5 = 0 0 + 6x + x2 = 5 + kx + -5 + x2 6x + x2 = 5 + kx + -5 + x2 Reorder the terms: 6x + x2 = 5 + -5 + kx + x2 Combine like terms: 5 + -5 = 0 6x + x2 = 0 + kx + x2 6x + x2 = kx + x2 Add '-1x2' to each side of the equation. 6x + x2 + -1x2 = kx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6x + 0 = kx + x2 + -1x2 6x = kx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6x = kx + 0 6x = kx Solving 6x = kx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1kx' to each side of the equation. -1kx + 6x = kx + -1kx Combine like terms: kx + -1kx = 0 -1kx + 6x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1k + 6) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1k + 6)' equal to zero and attempt to solve: Simplifying -1k + 6 = 0 Reorder the terms: 6 + -1k = 0 Solving 6 + -1k = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1k = 0 + -6 -1k = 0 + -6 Combine like terms: 0 + -6 = -6 -1k = -6 Add 'k' to each side of the equation. -1k + k = -6 + k Combine like terms: -1k + k = 0 0 = -6 + k Simplifying 0 = -6 + k The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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