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Simplifying (x + -7)(x + 4) + (x + -4)(x + -3) = 84 Reorder the terms: (-7 + x)(x + 4) + (x + -4)(x + -3) = 84 Reorder the terms: (-7 + x)(4 + x) + (x + -4)(x + -3) = 84 Multiply (-7 + x) * (4 + x) (-7(4 + x) + x(4 + x)) + (x + -4)(x + -3) = 84 ((4 * -7 + x * -7) + x(4 + x)) + (x + -4)(x + -3) = 84 ((-28 + -7x) + x(4 + x)) + (x + -4)(x + -3) = 84 (-28 + -7x + (4 * x + x * x)) + (x + -4)(x + -3) = 84 (-28 + -7x + (4x + x2)) + (x + -4)(x + -3) = 84 Combine like terms: -7x + 4x = -3x (-28 + -3x + x2) + (x + -4)(x + -3) = 84 Reorder the terms: -28 + -3x + x2 + (-4 + x)(x + -3) = 84 Reorder the terms: -28 + -3x + x2 + (-4 + x)(-3 + x) = 84 Multiply (-4 + x) * (-3 + x) -28 + -3x + x2 + (-4(-3 + x) + x(-3 + x)) = 84 -28 + -3x + x2 + ((-3 * -4 + x * -4) + x(-3 + x)) = 84 -28 + -3x + x2 + ((12 + -4x) + x(-3 + x)) = 84 -28 + -3x + x2 + (12 + -4x + (-3 * x + x * x)) = 84 -28 + -3x + x2 + (12 + -4x + (-3x + x2)) = 84 Combine like terms: -4x + -3x = -7x -28 + -3x + x2 + (12 + -7x + x2) = 84 Reorder the terms: -28 + 12 + -3x + -7x + x2 + x2 = 84 Combine like terms: -28 + 12 = -16 -16 + -3x + -7x + x2 + x2 = 84 Combine like terms: -3x + -7x = -10x -16 + -10x + x2 + x2 = 84 Combine like terms: x2 + x2 = 2x2 -16 + -10x + 2x2 = 84 Solving -16 + -10x + 2x2 = 84 Solving for variable 'x'. Reorder the terms: -16 + -84 + -10x + 2x2 = 84 + -84 Combine like terms: -16 + -84 = -100 -100 + -10x + 2x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -100 + -10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -5x + x2) = 0 Factor a trinomial. 2((-5 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-5, 10}
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