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Simplifying (2x + 3)(x + -7) = 2x + kx + -21 Reorder the terms: (3 + 2x)(x + -7) = 2x + kx + -21 Reorder the terms: (3 + 2x)(-7 + x) = 2x + kx + -21 Multiply (3 + 2x) * (-7 + x) (3(-7 + x) + 2x * (-7 + x)) = 2x + kx + -21 ((-7 * 3 + x * 3) + 2x * (-7 + x)) = 2x + kx + -21 ((-21 + 3x) + 2x * (-7 + x)) = 2x + kx + -21 (-21 + 3x + (-7 * 2x + x * 2x)) = 2x + kx + -21 (-21 + 3x + (-14x + 2x2)) = 2x + kx + -21 Combine like terms: 3x + -14x = -11x (-21 + -11x + 2x2) = 2x + kx + -21 Reorder the terms: -21 + -11x + 2x2 = -21 + kx + 2x Add '21' to each side of the equation. -21 + -11x + 21 + 2x2 = -21 + kx + 21 + 2x Reorder the terms: -21 + 21 + -11x + 2x2 = -21 + kx + 21 + 2x Combine like terms: -21 + 21 = 0 0 + -11x + 2x2 = -21 + kx + 21 + 2x -11x + 2x2 = -21 + kx + 21 + 2x Reorder the terms: -11x + 2x2 = -21 + 21 + kx + 2x Combine like terms: -21 + 21 = 0 -11x + 2x2 = 0 + kx + 2x -11x + 2x2 = kx + 2x Solving -11x + 2x2 = kx + 2x Solving for variable 'x'. Reorder the terms: -1kx + -11x + -2x + 2x2 = kx + 2x + -1kx + -2x Combine like terms: -11x + -2x = -13x -1kx + -13x + 2x2 = kx + 2x + -1kx + -2x Reorder the terms: -1kx + -13x + 2x2 = kx + -1kx + 2x + -2x Combine like terms: kx + -1kx = 0 -1kx + -13x + 2x2 = 0 + 2x + -2x -1kx + -13x + 2x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -1kx + -13x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1k + -13 + 2x) = 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 + -13 + 2x)' equal to zero and attempt to solve: Simplifying -1k + -13 + 2x = 0 Reorder the terms: -13 + -1k + 2x = 0 Solving -13 + -1k + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + -1k + 13 + 2x = 0 + 13 Reorder the terms: -13 + 13 + -1k + 2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1k + 2x = 0 + 13 -1k + 2x = 0 + 13 Combine like terms: 0 + 13 = 13 -1k + 2x = 13 Add 'k' to each side of the equation. -1k + k + 2x = 13 + k Combine like terms: -1k + k = 0 0 + 2x = 13 + k 2x = 13 + k Divide each side by '2'. x = 6.5 + 0.5k Simplifying x = 6.5 + 0.5kSolution
x = {0, 6.5 + 0.5k}
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