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Simplifying 0 = 80x3 + -45x Reorder the terms: 0 = -45x + 80x3 Solving 0 = -45x + 80x3 Solving for variable 'x'. Remove the zero: 45x + -80x3 = -45x + 80x3 + 45x + -80x3 Reorder the terms: 45x + -80x3 = -45x + 45x + 80x3 + -80x3 Combine like terms: -45x + 45x = 0 45x + -80x3 = 0 + 80x3 + -80x3 45x + -80x3 = 80x3 + -80x3 Combine like terms: 80x3 + -80x3 = 0 45x + -80x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(9 + -16x2) = 0 Factor a difference between two squares. 5x((3 + 4x)(3 + -4x)) = 0 Ignore the factor 5.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 '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Subproblem 3
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {0, -0.75, 0.75}
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