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Simplifying 2x2 + kx + -14 = (x + 2)(2x + -7) Reorder the terms: -14 + kx + 2x2 = (x + 2)(2x + -7) Reorder the terms: -14 + kx + 2x2 = (2 + x)(2x + -7) Reorder the terms: -14 + kx + 2x2 = (2 + x)(-7 + 2x) Multiply (2 + x) * (-7 + 2x) -14 + kx + 2x2 = (2(-7 + 2x) + x(-7 + 2x)) -14 + kx + 2x2 = ((-7 * 2 + 2x * 2) + x(-7 + 2x)) -14 + kx + 2x2 = ((-14 + 4x) + x(-7 + 2x)) -14 + kx + 2x2 = (-14 + 4x + (-7 * x + 2x * x)) -14 + kx + 2x2 = (-14 + 4x + (-7x + 2x2)) Combine like terms: 4x + -7x = -3x -14 + kx + 2x2 = (-14 + -3x + 2x2) Add '14' to each side of the equation. -14 + kx + 14 + 2x2 = -14 + -3x + 14 + 2x2 Reorder the terms: -14 + 14 + kx + 2x2 = -14 + -3x + 14 + 2x2 Combine like terms: -14 + 14 = 0 0 + kx + 2x2 = -14 + -3x + 14 + 2x2 kx + 2x2 = -14 + -3x + 14 + 2x2 Reorder the terms: kx + 2x2 = -14 + 14 + -3x + 2x2 Combine like terms: -14 + 14 = 0 kx + 2x2 = 0 + -3x + 2x2 kx + 2x2 = -3x + 2x2 Add '-2x2' to each side of the equation. kx + 2x2 + -2x2 = -3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 kx + 0 = -3x + 2x2 + -2x2 kx = -3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 kx = -3x + 0 kx = -3x Solving kx = -3x Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Divide each side by 'x'. k = -3 Simplifying k = -3
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