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Simplifying [(6x2 + 6x + 8) + -1(-3x2 + -8x + 2)] + -1(x2 + 9x + 6) = 0 Reorder the terms: [(8 + 6x + 6x2) + -1(-3x2 + -8x + 2)] + -1(x2 + 9x + 6) = 0 Remove parenthesis around (8 + 6x + 6x2) [8 + 6x + 6x2 + -1(-3x2 + -8x + 2)] + -1(x2 + 9x + 6) = 0 Reorder the terms: [8 + 6x + 6x2 + -1(2 + -8x + -3x2)] + -1(x2 + 9x + 6) = 0 [8 + 6x + 6x2 + (2 * -1 + -8x * -1 + -3x2 * -1)] + -1(x2 + 9x + 6) = 0 [8 + 6x + 6x2 + (-2 + 8x + 3x2)] + -1(x2 + 9x + 6) = 0 Reorder the terms: [8 + -2 + 6x + 8x + 6x2 + 3x2] + -1(x2 + 9x + 6) = 0 Combine like terms: 8 + -2 = 6 [6 + 6x + 8x + 6x2 + 3x2] + -1(x2 + 9x + 6) = 0 Combine like terms: 6x + 8x = 14x [6 + 14x + 6x2 + 3x2] + -1(x2 + 9x + 6) = 0 Combine like terms: 6x2 + 3x2 = 9x2 [6 + 14x + 9x2] + -1(x2 + 9x + 6) = 0 Remove brackets around [6 + 14x + 9x2] 6 + 14x + 9x2 + -1(x2 + 9x + 6) = 0 Reorder the terms: 6 + 14x + 9x2 + -1(6 + 9x + x2) = 0 6 + 14x + 9x2 + (6 * -1 + 9x * -1 + x2 * -1) = 0 6 + 14x + 9x2 + (-6 + -9x + -1x2) = 0 Reorder the terms: 6 + -6 + 14x + -9x + 9x2 + -1x2 = 0 Combine like terms: 6 + -6 = 0 0 + 14x + -9x + 9x2 + -1x2 = 0 14x + -9x + 9x2 + -1x2 = 0 Combine like terms: 14x + -9x = 5x 5x + 9x2 + -1x2 = 0 Combine like terms: 9x2 + -1x2 = 8x2 5x + 8x2 = 0 Solving 5x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 8x) = 0Subproblem 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 '(5 + 8x)' equal to zero and attempt to solve: Simplifying 5 + 8x = 0 Solving 5 + 8x = 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 + 8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x = 0 + -5 8x = 0 + -5 Combine like terms: 0 + -5 = -5 8x = -5 Divide each side by '8'. x = -0.625 Simplifying x = -0.625Solution
x = {0, -0.625}
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