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Simplifying ((3x + -3)(3x + -3)) + -1((4x + 1)(4x + 1)) = 8 Reorder the terms: ((-3 + 3x)(3x + -3)) + -1((4x + 1)(4x + 1)) = 8 Reorder the terms: ((-3 + 3x)(-3 + 3x)) + -1((4x + 1)(4x + 1)) = 8 Multiply (-3 + 3x) * (-3 + 3x) ((-3(-3 + 3x) + 3x * (-3 + 3x))) + -1((4x + 1)(4x + 1)) = 8 (((-3 * -3 + 3x * -3) + 3x * (-3 + 3x))) + -1((4x + 1)(4x + 1)) = 8 (((9 + -9x) + 3x * (-3 + 3x))) + -1((4x + 1)(4x + 1)) = 8 ((9 + -9x + (-3 * 3x + 3x * 3x))) + -1((4x + 1)(4x + 1)) = 8 ((9 + -9x + (-9x + 9x2))) + -1((4x + 1)(4x + 1)) = 8 Combine like terms: -9x + -9x = -18x ((9 + -18x + 9x2)) + -1((4x + 1)(4x + 1)) = 8 (9 + -18x + 9x2) + -1((4x + 1)(4x + 1)) = 8 Remove parenthesis around (9 + -18x + 9x2) 9 + -18x + 9x2 + -1((4x + 1)(4x + 1)) = 8 Reorder the terms: 9 + -18x + 9x2 + -1((1 + 4x)(4x + 1)) = 8 Reorder the terms: 9 + -18x + 9x2 + -1((1 + 4x)(1 + 4x)) = 8 Multiply (1 + 4x) * (1 + 4x) 9 + -18x + 9x2 + -1((1(1 + 4x) + 4x * (1 + 4x))) = 8 9 + -18x + 9x2 + -1(((1 * 1 + 4x * 1) + 4x * (1 + 4x))) = 8 9 + -18x + 9x2 + -1(((1 + 4x) + 4x * (1 + 4x))) = 8 9 + -18x + 9x2 + -1((1 + 4x + (1 * 4x + 4x * 4x))) = 8 9 + -18x + 9x2 + -1((1 + 4x + (4x + 16x2))) = 8 Combine like terms: 4x + 4x = 8x 9 + -18x + 9x2 + -1((1 + 8x + 16x2)) = 8 9 + -18x + 9x2 + (1 * -1 + 8x * -1 + 16x2 * -1) = 8 9 + -18x + 9x2 + (-1 + -8x + -16x2) = 8 Reorder the terms: 9 + -1 + -18x + -8x + 9x2 + -16x2 = 8 Combine like terms: 9 + -1 = 8 8 + -18x + -8x + 9x2 + -16x2 = 8 Combine like terms: -18x + -8x = -26x 8 + -26x + 9x2 + -16x2 = 8 Combine like terms: 9x2 + -16x2 = -7x2 8 + -26x + -7x2 = 8 Add '-8' to each side of the equation. 8 + -26x + -8 + -7x2 = 8 + -8 Reorder the terms: 8 + -8 + -26x + -7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 0 + -26x + -7x2 = 8 + -8 -26x + -7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -26x + -7x2 = 0 Solving -26x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(26 + 7x) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(26 + 7x)' equal to zero and attempt to solve: Simplifying 26 + 7x = 0 Solving 26 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-26' to each side of the equation. 26 + -26 + 7x = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 7x = 0 + -26 7x = 0 + -26 Combine like terms: 0 + -26 = -26 7x = -26 Divide each side by '7'. x = -3.714285714 Simplifying x = -3.714285714Solution
x = {0, -3.714285714}
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