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Simplifying (x + -4)(x + -4) + -1(2x + -11)(2x + -11) = 3 Reorder the terms: (-4 + x)(x + -4) + -1(2x + -11)(2x + -11) = 3 Reorder the terms: (-4 + x)(-4 + x) + -1(2x + -11)(2x + -11) = 3 Multiply (-4 + x) * (-4 + x) (-4(-4 + x) + x(-4 + x)) + -1(2x + -11)(2x + -11) = 3 ((-4 * -4 + x * -4) + x(-4 + x)) + -1(2x + -11)(2x + -11) = 3 ((16 + -4x) + x(-4 + x)) + -1(2x + -11)(2x + -11) = 3 (16 + -4x + (-4 * x + x * x)) + -1(2x + -11)(2x + -11) = 3 (16 + -4x + (-4x + x2)) + -1(2x + -11)(2x + -11) = 3 Combine like terms: -4x + -4x = -8x (16 + -8x + x2) + -1(2x + -11)(2x + -11) = 3 Reorder the terms: 16 + -8x + x2 + -1(-11 + 2x)(2x + -11) = 3 Reorder the terms: 16 + -8x + x2 + -1(-11 + 2x)(-11 + 2x) = 3 Multiply (-11 + 2x) * (-11 + 2x) 16 + -8x + x2 + -1(-11(-11 + 2x) + 2x * (-11 + 2x)) = 3 16 + -8x + x2 + -1((-11 * -11 + 2x * -11) + 2x * (-11 + 2x)) = 3 16 + -8x + x2 + -1((121 + -22x) + 2x * (-11 + 2x)) = 3 16 + -8x + x2 + -1(121 + -22x + (-11 * 2x + 2x * 2x)) = 3 16 + -8x + x2 + -1(121 + -22x + (-22x + 4x2)) = 3 Combine like terms: -22x + -22x = -44x 16 + -8x + x2 + -1(121 + -44x + 4x2) = 3 16 + -8x + x2 + (121 * -1 + -44x * -1 + 4x2 * -1) = 3 16 + -8x + x2 + (-121 + 44x + -4x2) = 3 Reorder the terms: 16 + -121 + -8x + 44x + x2 + -4x2 = 3 Combine like terms: 16 + -121 = -105 -105 + -8x + 44x + x2 + -4x2 = 3 Combine like terms: -8x + 44x = 36x -105 + 36x + x2 + -4x2 = 3 Combine like terms: x2 + -4x2 = -3x2 -105 + 36x + -3x2 = 3 Solving -105 + 36x + -3x2 = 3 Solving for variable 'x'. Reorder the terms: -105 + -3 + 36x + -3x2 = 3 + -3 Combine like terms: -105 + -3 = -108 -108 + 36x + -3x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -108 + 36x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + 12x + -1x2) = 0 Factor a trinomial. 3((-6 + x)(6 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 6}
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