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Simplifying (4x + -5)(4x + -5) + -1(3x + 7)(3x + 7) = 0 Reorder the terms: (-5 + 4x)(4x + -5) + -1(3x + 7)(3x + 7) = 0 Reorder the terms: (-5 + 4x)(-5 + 4x) + -1(3x + 7)(3x + 7) = 0 Multiply (-5 + 4x) * (-5 + 4x) (-5(-5 + 4x) + 4x * (-5 + 4x)) + -1(3x + 7)(3x + 7) = 0 ((-5 * -5 + 4x * -5) + 4x * (-5 + 4x)) + -1(3x + 7)(3x + 7) = 0 ((25 + -20x) + 4x * (-5 + 4x)) + -1(3x + 7)(3x + 7) = 0 (25 + -20x + (-5 * 4x + 4x * 4x)) + -1(3x + 7)(3x + 7) = 0 (25 + -20x + (-20x + 16x2)) + -1(3x + 7)(3x + 7) = 0 Combine like terms: -20x + -20x = -40x (25 + -40x + 16x2) + -1(3x + 7)(3x + 7) = 0 Reorder the terms: 25 + -40x + 16x2 + -1(7 + 3x)(3x + 7) = 0 Reorder the terms: 25 + -40x + 16x2 + -1(7 + 3x)(7 + 3x) = 0 Multiply (7 + 3x) * (7 + 3x) 25 + -40x + 16x2 + -1(7(7 + 3x) + 3x * (7 + 3x)) = 0 25 + -40x + 16x2 + -1((7 * 7 + 3x * 7) + 3x * (7 + 3x)) = 0 25 + -40x + 16x2 + -1((49 + 21x) + 3x * (7 + 3x)) = 0 25 + -40x + 16x2 + -1(49 + 21x + (7 * 3x + 3x * 3x)) = 0 25 + -40x + 16x2 + -1(49 + 21x + (21x + 9x2)) = 0 Combine like terms: 21x + 21x = 42x 25 + -40x + 16x2 + -1(49 + 42x + 9x2) = 0 25 + -40x + 16x2 + (49 * -1 + 42x * -1 + 9x2 * -1) = 0 25 + -40x + 16x2 + (-49 + -42x + -9x2) = 0 Reorder the terms: 25 + -49 + -40x + -42x + 16x2 + -9x2 = 0 Combine like terms: 25 + -49 = -24 -24 + -40x + -42x + 16x2 + -9x2 = 0 Combine like terms: -40x + -42x = -82x -24 + -82x + 16x2 + -9x2 = 0 Combine like terms: 16x2 + -9x2 = 7x2 -24 + -82x + 7x2 = 0 Solving -24 + -82x + 7x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + -7x)(12 + -1x) = 0Subproblem 1
Set the factor '(-2 + -7x)' equal to zero and attempt to solve: Simplifying -2 + -7x = 0 Solving -2 + -7x = 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 + -7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7x = 0 + 2 -7x = 0 + 2 Combine like terms: 0 + 2 = 2 -7x = 2 Divide each side by '-7'. x = -0.2857142857 Simplifying x = -0.2857142857Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-0.2857142857, 12}
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