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Simplifying 7(x + -4)(x + -4) + -18 = 10 Reorder the terms: 7(-4 + x)(x + -4) + -18 = 10 Reorder the terms: 7(-4 + x)(-4 + x) + -18 = 10 Multiply (-4 + x) * (-4 + x) 7(-4(-4 + x) + x(-4 + x)) + -18 = 10 7((-4 * -4 + x * -4) + x(-4 + x)) + -18 = 10 7((16 + -4x) + x(-4 + x)) + -18 = 10 7(16 + -4x + (-4 * x + x * x)) + -18 = 10 7(16 + -4x + (-4x + x2)) + -18 = 10 Combine like terms: -4x + -4x = -8x 7(16 + -8x + x2) + -18 = 10 (16 * 7 + -8x * 7 + x2 * 7) + -18 = 10 (112 + -56x + 7x2) + -18 = 10 Reorder the terms: 112 + -18 + -56x + 7x2 = 10 Combine like terms: 112 + -18 = 94 94 + -56x + 7x2 = 10 Solving 94 + -56x + 7x2 = 10 Solving for variable 'x'. Reorder the terms: 94 + -10 + -56x + 7x2 = 10 + -10 Combine like terms: 94 + -10 = 84 84 + -56x + 7x2 = 10 + -10 Combine like terms: 10 + -10 = 0 84 + -56x + 7x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(12 + -8x + x2) = 0 Factor a trinomial. 7((2 + -1x)(6 + -1x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {2, 6}
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