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Simplifying (3x + -4)(3x + -4) + -1(6x + -7)(6x + -7) = 0 Reorder the terms: (-4 + 3x)(3x + -4) + -1(6x + -7)(6x + -7) = 0 Reorder the terms: (-4 + 3x)(-4 + 3x) + -1(6x + -7)(6x + -7) = 0 Multiply (-4 + 3x) * (-4 + 3x) (-4(-4 + 3x) + 3x * (-4 + 3x)) + -1(6x + -7)(6x + -7) = 0 ((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) + -1(6x + -7)(6x + -7) = 0 ((16 + -12x) + 3x * (-4 + 3x)) + -1(6x + -7)(6x + -7) = 0 (16 + -12x + (-4 * 3x + 3x * 3x)) + -1(6x + -7)(6x + -7) = 0 (16 + -12x + (-12x + 9x2)) + -1(6x + -7)(6x + -7) = 0 Combine like terms: -12x + -12x = -24x (16 + -24x + 9x2) + -1(6x + -7)(6x + -7) = 0 Reorder the terms: 16 + -24x + 9x2 + -1(-7 + 6x)(6x + -7) = 0 Reorder the terms: 16 + -24x + 9x2 + -1(-7 + 6x)(-7 + 6x) = 0 Multiply (-7 + 6x) * (-7 + 6x) 16 + -24x + 9x2 + -1(-7(-7 + 6x) + 6x * (-7 + 6x)) = 0 16 + -24x + 9x2 + -1((-7 * -7 + 6x * -7) + 6x * (-7 + 6x)) = 0 16 + -24x + 9x2 + -1((49 + -42x) + 6x * (-7 + 6x)) = 0 16 + -24x + 9x2 + -1(49 + -42x + (-7 * 6x + 6x * 6x)) = 0 16 + -24x + 9x2 + -1(49 + -42x + (-42x + 36x2)) = 0 Combine like terms: -42x + -42x = -84x 16 + -24x + 9x2 + -1(49 + -84x + 36x2) = 0 16 + -24x + 9x2 + (49 * -1 + -84x * -1 + 36x2 * -1) = 0 16 + -24x + 9x2 + (-49 + 84x + -36x2) = 0 Reorder the terms: 16 + -49 + -24x + 84x + 9x2 + -36x2 = 0 Combine like terms: 16 + -49 = -33 -33 + -24x + 84x + 9x2 + -36x2 = 0 Combine like terms: -24x + 84x = 60x -33 + 60x + 9x2 + -36x2 = 0 Combine like terms: 9x2 + -36x2 = -27x2 -33 + 60x + -27x2 = 0 Solving -33 + 60x + -27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 20x + -9x2) = 0 Factor a trinomial. 3((-11 + 9x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + 9x)' equal to zero and attempt to solve: Simplifying -11 + 9x = 0 Solving -11 + 9x = 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 + 9x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 9x = 0 + 11 9x = 0 + 11 Combine like terms: 0 + 11 = 11 9x = 11 Divide each side by '9'. x = 1.222222222 Simplifying x = 1.222222222Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1.222222222, 1}
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