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Simplifying [(-2x2 + 4x + 5) + -1(-9x2 + 9x + 8)] + -1(x2 + 6x + -3) = 0 Reorder the terms: [(5 + 4x + -2x2) + -1(-9x2 + 9x + 8)] + -1(x2 + 6x + -3) = 0 Remove parenthesis around (5 + 4x + -2x2) [5 + 4x + -2x2 + -1(-9x2 + 9x + 8)] + -1(x2 + 6x + -3) = 0 Reorder the terms: [5 + 4x + -2x2 + -1(8 + 9x + -9x2)] + -1(x2 + 6x + -3) = 0 [5 + 4x + -2x2 + (8 * -1 + 9x * -1 + -9x2 * -1)] + -1(x2 + 6x + -3) = 0 [5 + 4x + -2x2 + (-8 + -9x + 9x2)] + -1(x2 + 6x + -3) = 0 Reorder the terms: [5 + -8 + 4x + -9x + -2x2 + 9x2] + -1(x2 + 6x + -3) = 0 Combine like terms: 5 + -8 = -3 [-3 + 4x + -9x + -2x2 + 9x2] + -1(x2 + 6x + -3) = 0 Combine like terms: 4x + -9x = -5x [-3 + -5x + -2x2 + 9x2] + -1(x2 + 6x + -3) = 0 Combine like terms: -2x2 + 9x2 = 7x2 [-3 + -5x + 7x2] + -1(x2 + 6x + -3) = 0 Remove brackets around [-3 + -5x + 7x2] -3 + -5x + 7x2 + -1(x2 + 6x + -3) = 0 Reorder the terms: -3 + -5x + 7x2 + -1(-3 + 6x + x2) = 0 -3 + -5x + 7x2 + (-3 * -1 + 6x * -1 + x2 * -1) = 0 -3 + -5x + 7x2 + (3 + -6x + -1x2) = 0 Reorder the terms: -3 + 3 + -5x + -6x + 7x2 + -1x2 = 0 Combine like terms: -3 + 3 = 0 0 + -5x + -6x + 7x2 + -1x2 = 0 -5x + -6x + 7x2 + -1x2 = 0 Combine like terms: -5x + -6x = -11x -11x + 7x2 + -1x2 = 0 Combine like terms: 7x2 + -1x2 = 6x2 -11x + 6x2 = 0 Solving -11x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 6x) = 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 '(-11 + 6x)' equal to zero and attempt to solve: Simplifying -11 + 6x = 0 Solving -11 + 6x = 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 + 6x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 6x = 0 + 11 6x = 0 + 11 Combine like terms: 0 + 11 = 11 6x = 11 Divide each side by '6'. x = 1.833333333 Simplifying x = 1.833333333Solution
x = {0, 1.833333333}
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