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Simplifying (x + 4)(x + 4) + -1(3x + -7)(3x + -7) = 0 Reorder the terms: (4 + x)(x + 4) + -1(3x + -7)(3x + -7) = 0 Reorder the terms: (4 + x)(4 + x) + -1(3x + -7)(3x + -7) = 0 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) + -1(3x + -7)(3x + -7) = 0 ((4 * 4 + x * 4) + x(4 + x)) + -1(3x + -7)(3x + -7) = 0 ((16 + 4x) + x(4 + x)) + -1(3x + -7)(3x + -7) = 0 (16 + 4x + (4 * x + x * x)) + -1(3x + -7)(3x + -7) = 0 (16 + 4x + (4x + x2)) + -1(3x + -7)(3x + -7) = 0 Combine like terms: 4x + 4x = 8x (16 + 8x + x2) + -1(3x + -7)(3x + -7) = 0 Reorder the terms: 16 + 8x + x2 + -1(-7 + 3x)(3x + -7) = 0 Reorder the terms: 16 + 8x + x2 + -1(-7 + 3x)(-7 + 3x) = 0 Multiply (-7 + 3x) * (-7 + 3x) 16 + 8x + x2 + -1(-7(-7 + 3x) + 3x * (-7 + 3x)) = 0 16 + 8x + x2 + -1((-7 * -7 + 3x * -7) + 3x * (-7 + 3x)) = 0 16 + 8x + x2 + -1((49 + -21x) + 3x * (-7 + 3x)) = 0 16 + 8x + x2 + -1(49 + -21x + (-7 * 3x + 3x * 3x)) = 0 16 + 8x + x2 + -1(49 + -21x + (-21x + 9x2)) = 0 Combine like terms: -21x + -21x = -42x 16 + 8x + x2 + -1(49 + -42x + 9x2) = 0 16 + 8x + x2 + (49 * -1 + -42x * -1 + 9x2 * -1) = 0 16 + 8x + x2 + (-49 + 42x + -9x2) = 0 Reorder the terms: 16 + -49 + 8x + 42x + x2 + -9x2 = 0 Combine like terms: 16 + -49 = -33 -33 + 8x + 42x + x2 + -9x2 = 0 Combine like terms: 8x + 42x = 50x -33 + 50x + x2 + -9x2 = 0 Combine like terms: x2 + -9x2 = -8x2 -33 + 50x + -8x2 = 0 Solving -33 + 50x + -8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-11 + 2x)(3 + -4x) = 0Subproblem 1
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 = 5.5Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {5.5, 0.75}
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