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Simplifying (6x + 7)(6x + 7) = (9x + -8)(9x + -8) Reorder the terms: (7 + 6x)(6x + 7) = (9x + -8)(9x + -8) Reorder the terms: (7 + 6x)(7 + 6x) = (9x + -8)(9x + -8) Multiply (7 + 6x) * (7 + 6x) (7(7 + 6x) + 6x * (7 + 6x)) = (9x + -8)(9x + -8) ((7 * 7 + 6x * 7) + 6x * (7 + 6x)) = (9x + -8)(9x + -8) ((49 + 42x) + 6x * (7 + 6x)) = (9x + -8)(9x + -8) (49 + 42x + (7 * 6x + 6x * 6x)) = (9x + -8)(9x + -8) (49 + 42x + (42x + 36x2)) = (9x + -8)(9x + -8) Combine like terms: 42x + 42x = 84x (49 + 84x + 36x2) = (9x + -8)(9x + -8) Reorder the terms: 49 + 84x + 36x2 = (-8 + 9x)(9x + -8) Reorder the terms: 49 + 84x + 36x2 = (-8 + 9x)(-8 + 9x) Multiply (-8 + 9x) * (-8 + 9x) 49 + 84x + 36x2 = (-8(-8 + 9x) + 9x * (-8 + 9x)) 49 + 84x + 36x2 = ((-8 * -8 + 9x * -8) + 9x * (-8 + 9x)) 49 + 84x + 36x2 = ((64 + -72x) + 9x * (-8 + 9x)) 49 + 84x + 36x2 = (64 + -72x + (-8 * 9x + 9x * 9x)) 49 + 84x + 36x2 = (64 + -72x + (-72x + 81x2)) Combine like terms: -72x + -72x = -144x 49 + 84x + 36x2 = (64 + -144x + 81x2) Solving 49 + 84x + 36x2 = 64 + -144x + 81x2 Solving for variable 'x'. Reorder the terms: 49 + -64 + 84x + 144x + 36x2 + -81x2 = 64 + -144x + 81x2 + -64 + 144x + -81x2 Combine like terms: 49 + -64 = -15 -15 + 84x + 144x + 36x2 + -81x2 = 64 + -144x + 81x2 + -64 + 144x + -81x2 Combine like terms: 84x + 144x = 228x -15 + 228x + 36x2 + -81x2 = 64 + -144x + 81x2 + -64 + 144x + -81x2 Combine like terms: 36x2 + -81x2 = -45x2 -15 + 228x + -45x2 = 64 + -144x + 81x2 + -64 + 144x + -81x2 Reorder the terms: -15 + 228x + -45x2 = 64 + -64 + -144x + 144x + 81x2 + -81x2 Combine like terms: 64 + -64 = 0 -15 + 228x + -45x2 = 0 + -144x + 144x + 81x2 + -81x2 -15 + 228x + -45x2 = -144x + 144x + 81x2 + -81x2 Combine like terms: -144x + 144x = 0 -15 + 228x + -45x2 = 0 + 81x2 + -81x2 -15 + 228x + -45x2 = 81x2 + -81x2 Combine like terms: 81x2 + -81x2 = 0 -15 + 228x + -45x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 76x + -15x2) = 0 Factor a trinomial. 3((-5 + x)(1 + -15x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(1 + -15x)' equal to zero and attempt to solve: Simplifying 1 + -15x = 0 Solving 1 + -15x = 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 + -15x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -15x = 0 + -1 -15x = 0 + -1 Combine like terms: 0 + -1 = -1 -15x = -1 Divide each side by '-15'. x = 0.06666666667 Simplifying x = 0.06666666667Solution
x = {5, 0.06666666667}
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