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Simplifying -1x2 + -1(k + 7) * x + -8 = -1(x + -2)(x + -4) Reorder the terms: -1x2 + -1(7 + k) * x + -8 = -1(x + -2)(x + -4) Reorder the terms for easier multiplication: -1x2 + -1x(7 + k) + -8 = -1(x + -2)(x + -4) -1x2 + (7 * -1x + k * -1x) + -8 = -1(x + -2)(x + -4) Reorder the terms: -1x2 + (-1kx + -7x) + -8 = -1(x + -2)(x + -4) -1x2 + (-1kx + -7x) + -8 = -1(x + -2)(x + -4) Reorder the terms: -8 + -1kx + -7x + -1x2 = -1(x + -2)(x + -4) Reorder the terms: -8 + -1kx + -7x + -1x2 = -1(-2 + x)(x + -4) Reorder the terms: -8 + -1kx + -7x + -1x2 = -1(-2 + x)(-4 + x) Multiply (-2 + x) * (-4 + x) -8 + -1kx + -7x + -1x2 = -1(-2(-4 + x) + x(-4 + x)) -8 + -1kx + -7x + -1x2 = -1((-4 * -2 + x * -2) + x(-4 + x)) -8 + -1kx + -7x + -1x2 = -1((8 + -2x) + x(-4 + x)) -8 + -1kx + -7x + -1x2 = -1(8 + -2x + (-4 * x + x * x)) -8 + -1kx + -7x + -1x2 = -1(8 + -2x + (-4x + x2)) Combine like terms: -2x + -4x = -6x -8 + -1kx + -7x + -1x2 = -1(8 + -6x + x2) -8 + -1kx + -7x + -1x2 = (8 * -1 + -6x * -1 + x2 * -1) -8 + -1kx + -7x + -1x2 = (-8 + 6x + -1x2) Add '8' to each side of the equation. -8 + -1kx + -7x + 8 + -1x2 = -8 + 6x + 8 + -1x2 Reorder the terms: -8 + 8 + -1kx + -7x + -1x2 = -8 + 6x + 8 + -1x2 Combine like terms: -8 + 8 = 0 0 + -1kx + -7x + -1x2 = -8 + 6x + 8 + -1x2 -1kx + -7x + -1x2 = -8 + 6x + 8 + -1x2 Reorder the terms: -1kx + -7x + -1x2 = -8 + 8 + 6x + -1x2 Combine like terms: -8 + 8 = 0 -1kx + -7x + -1x2 = 0 + 6x + -1x2 -1kx + -7x + -1x2 = 6x + -1x2 Add 'x2' to each side of the equation. -1kx + -7x + -1x2 + x2 = 6x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1kx + -7x + 0 = 6x + -1x2 + x2 -1kx + -7x = 6x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1kx + -7x = 6x + 0 -1kx + -7x = 6x Solving -1kx + -7x = 6x Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '7x' to each side of the equation. -1kx + -7x + 7x = 6x + 7x Combine like terms: -7x + 7x = 0 -1kx + 0 = 6x + 7x -1kx = 6x + 7x Combine like terms: 6x + 7x = 13x -1kx = 13x Divide each side by '-1x'. k = -13 Simplifying k = -13
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