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Simplifying (7x + -4)(2x + -11) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Reorder the terms: (-4 + 7x)(2x + -11) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Reorder the terms: (-4 + 7x)(-11 + 2x) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Multiply (-4 + 7x) * (-11 + 2x) (-4(-11 + 2x) + 7x * (-11 + 2x)) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 ((-11 * -4 + 2x * -4) + 7x * (-11 + 2x)) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 ((44 + -8x) + 7x * (-11 + 2x)) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 (44 + -8x + (-11 * 7x + 2x * 7x)) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 (44 + -8x + (-77x + 14x2)) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Combine like terms: -8x + -77x = -85x (44 + -85x + 14x2) + -1(6x + 7)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Reorder the terms: 44 + -85x + 14x2 + -1(7 + 6x)(2x + -11) + -1(7x + -5)(11 + -2x) = 0 Reorder the terms: 44 + -85x + 14x2 + -1(7 + 6x)(-11 + 2x) + -1(7x + -5)(11 + -2x) = 0 Multiply (7 + 6x) * (-11 + 2x) 44 + -85x + 14x2 + -1(7(-11 + 2x) + 6x * (-11 + 2x)) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + -1((-11 * 7 + 2x * 7) + 6x * (-11 + 2x)) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + -1((-77 + 14x) + 6x * (-11 + 2x)) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + -1(-77 + 14x + (-11 * 6x + 2x * 6x)) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + -1(-77 + 14x + (-66x + 12x2)) + -1(7x + -5)(11 + -2x) = 0 Combine like terms: 14x + -66x = -52x 44 + -85x + 14x2 + -1(-77 + -52x + 12x2) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + (-77 * -1 + -52x * -1 + 12x2 * -1) + -1(7x + -5)(11 + -2x) = 0 44 + -85x + 14x2 + (77 + 52x + -12x2) + -1(7x + -5)(11 + -2x) = 0 Reorder the terms: 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1(-5 + 7x)(11 + -2x) = 0 Multiply (-5 + 7x) * (11 + -2x) 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1(-5(11 + -2x) + 7x * (11 + -2x)) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1((11 * -5 + -2x * -5) + 7x * (11 + -2x)) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1((-55 + 10x) + 7x * (11 + -2x)) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1(-55 + 10x + (11 * 7x + -2x * 7x)) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1(-55 + 10x + (77x + -14x2)) = 0 Combine like terms: 10x + 77x = 87x 44 + -85x + 14x2 + 77 + 52x + -12x2 + -1(-55 + 87x + -14x2) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + (-55 * -1 + 87x * -1 + -14x2 * -1) = 0 44 + -85x + 14x2 + 77 + 52x + -12x2 + (55 + -87x + 14x2) = 0 Reorder the terms: 44 + 77 + 55 + -85x + 52x + -87x + 14x2 + -12x2 + 14x2 = 0 Combine like terms: 44 + 77 = 121 121 + 55 + -85x + 52x + -87x + 14x2 + -12x2 + 14x2 = 0 Combine like terms: 121 + 55 = 176 176 + -85x + 52x + -87x + 14x2 + -12x2 + 14x2 = 0 Combine like terms: -85x + 52x = -33x 176 + -33x + -87x + 14x2 + -12x2 + 14x2 = 0 Combine like terms: -33x + -87x = -120x 176 + -120x + 14x2 + -12x2 + 14x2 = 0 Combine like terms: 14x2 + -12x2 = 2x2 176 + -120x + 2x2 + 14x2 = 0 Combine like terms: 2x2 + 14x2 = 16x2 176 + -120x + 16x2 = 0 Solving 176 + -120x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(22 + -15x + 2x2) = 0 Factor a trinomial. 8((2 + -1x)(11 + -2x)) = 0 Ignore the factor 8.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 '(11 + -2x)' equal to zero and attempt to solve: Simplifying 11 + -2x = 0 Solving 11 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2x = 0 + -11 -2x = 0 + -11 Combine like terms: 0 + -11 = -11 -2x = -11 Divide each side by '-2'. x = 5.5 Simplifying x = 5.5Solution
x = {2, 5.5}
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