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Simplifying (2x + -5)(x + -2) = 2x2 + kx + 10 Reorder the terms: (-5 + 2x)(x + -2) = 2x2 + kx + 10 Reorder the terms: (-5 + 2x)(-2 + x) = 2x2 + kx + 10 Multiply (-5 + 2x) * (-2 + x) (-5(-2 + x) + 2x * (-2 + x)) = 2x2 + kx + 10 ((-2 * -5 + x * -5) + 2x * (-2 + x)) = 2x2 + kx + 10 ((10 + -5x) + 2x * (-2 + x)) = 2x2 + kx + 10 (10 + -5x + (-2 * 2x + x * 2x)) = 2x2 + kx + 10 (10 + -5x + (-4x + 2x2)) = 2x2 + kx + 10 Combine like terms: -5x + -4x = -9x (10 + -9x + 2x2) = 2x2 + kx + 10 Reorder the terms: 10 + -9x + 2x2 = 10 + kx + 2x2 Add '-10' to each side of the equation. 10 + -9x + -10 + 2x2 = 10 + kx + -10 + 2x2 Reorder the terms: 10 + -10 + -9x + 2x2 = 10 + kx + -10 + 2x2 Combine like terms: 10 + -10 = 0 0 + -9x + 2x2 = 10 + kx + -10 + 2x2 -9x + 2x2 = 10 + kx + -10 + 2x2 Reorder the terms: -9x + 2x2 = 10 + -10 + kx + 2x2 Combine like terms: 10 + -10 = 0 -9x + 2x2 = 0 + kx + 2x2 -9x + 2x2 = kx + 2x2 Add '-2x2' to each side of the equation. -9x + 2x2 + -2x2 = kx + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9x + 0 = kx + 2x2 + -2x2 -9x = kx + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -9x = kx + 0 -9x = kx Solving -9x = 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 + -9x = kx + -1kx Combine like terms: kx + -1kx = 0 -1kx + -9x = 0 Factor out the Greatest Common Factor (GCF), '-1x'. -1x(k + 9) = 0 Ignore the factor -1.Subproblem 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 '(k + 9)' equal to zero and attempt to solve: Simplifying k + 9 = 0 Reorder the terms: 9 + k = 0 Solving 9 + k = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + k = 0 + -9 Combine like terms: 9 + -9 = 0 0 + k = 0 + -9 k = 0 + -9 Combine like terms: 0 + -9 = -9 k = -9 Add '-1k' to each side of the equation. k + -1k = -9 + -1k Combine like terms: k + -1k = 0 0 = -9 + -1k Simplifying 0 = -9 + -1k 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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