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Simplifying 5x3 + -35x2 + 115x = 0 Reorder the terms: 115x + -35x2 + 5x3 = 0 Solving 115x + -35x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(23 + -7x + x2) = 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 '(23 + -7x + x2)' equal to zero and attempt to solve: Simplifying 23 + -7x + x2 = 0 Solving 23 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -7x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -7x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -7x + x2 = 0 + -23 -7x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -7x + x2 = -23 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -23 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -23 + 12.25 Combine like terms: -23 + 12.25 = -10.75 12.25 + -7x + x2 = -10.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -10.75 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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