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Simplifying 35x3 + -25x2 + 40x = 0 Reorder the terms: 40x + -25x2 + 35x3 = 0 Solving 40x + -25x2 + 35x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(8 + -5x + 7x2) = 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 '(8 + -5x + 7x2)' equal to zero and attempt to solve: Simplifying 8 + -5x + 7x2 = 0 Solving 8 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.142857143 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -0.7142857143x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -0.7142857143x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + -1.142857143 -0.7142857143x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -0.7142857143x + x2 = -1.142857143 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = -1.142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = -1.142857143 + 0.1275510204 Combine like terms: -1.142857143 + 0.1275510204 = -1.0153061226 0.1275510204 + -0.7142857143x + x2 = -1.0153061226 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = -1.0153061226 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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