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Simplifying [(-5x2 + 8x + -3) + -1(6x2 + -11x + 4)] + -1(x2 + 9x + -7) = 0 Reorder the terms: [(-3 + 8x + -5x2) + -1(6x2 + -11x + 4)] + -1(x2 + 9x + -7) = 0 Remove parenthesis around (-3 + 8x + -5x2) [-3 + 8x + -5x2 + -1(6x2 + -11x + 4)] + -1(x2 + 9x + -7) = 0 Reorder the terms: [-3 + 8x + -5x2 + -1(4 + -11x + 6x2)] + -1(x2 + 9x + -7) = 0 [-3 + 8x + -5x2 + (4 * -1 + -11x * -1 + 6x2 * -1)] + -1(x2 + 9x + -7) = 0 [-3 + 8x + -5x2 + (-4 + 11x + -6x2)] + -1(x2 + 9x + -7) = 0 Reorder the terms: [-3 + -4 + 8x + 11x + -5x2 + -6x2] + -1(x2 + 9x + -7) = 0 Combine like terms: -3 + -4 = -7 [-7 + 8x + 11x + -5x2 + -6x2] + -1(x2 + 9x + -7) = 0 Combine like terms: 8x + 11x = 19x [-7 + 19x + -5x2 + -6x2] + -1(x2 + 9x + -7) = 0 Combine like terms: -5x2 + -6x2 = -11x2 [-7 + 19x + -11x2] + -1(x2 + 9x + -7) = 0 Remove brackets around [-7 + 19x + -11x2] -7 + 19x + -11x2 + -1(x2 + 9x + -7) = 0 Reorder the terms: -7 + 19x + -11x2 + -1(-7 + 9x + x2) = 0 -7 + 19x + -11x2 + (-7 * -1 + 9x * -1 + x2 * -1) = 0 -7 + 19x + -11x2 + (7 + -9x + -1x2) = 0 Reorder the terms: -7 + 7 + 19x + -9x + -11x2 + -1x2 = 0 Combine like terms: -7 + 7 = 0 0 + 19x + -9x + -11x2 + -1x2 = 0 19x + -9x + -11x2 + -1x2 = 0 Combine like terms: 19x + -9x = 10x 10x + -11x2 + -1x2 = 0 Combine like terms: -11x2 + -1x2 = -12x2 10x + -12x2 = 0 Solving 10x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + -6x) = 0 Ignore the factor 2.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 '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 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 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {0, 0.8333333333}
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