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Simplifying 8x(4x + -7) + -5(6x2 + -11x) = 0 Reorder the terms: 8x(-7 + 4x) + -5(6x2 + -11x) = 0 (-7 * 8x + 4x * 8x) + -5(6x2 + -11x) = 0 (-56x + 32x2) + -5(6x2 + -11x) = 0 Reorder the terms: -56x + 32x2 + -5(-11x + 6x2) = 0 -56x + 32x2 + (-11x * -5 + 6x2 * -5) = 0 -56x + 32x2 + (55x + -30x2) = 0 Reorder the terms: -56x + 55x + 32x2 + -30x2 = 0 Combine like terms: -56x + 55x = -1x -1x + 32x2 + -30x2 = 0 Combine like terms: 32x2 + -30x2 = 2x2 -1x + 2x2 = 0 Solving -1x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 2x) = 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 '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Solution
x = {0, 0.5}
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