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Simplifying 3x3 + -15x2 + 4x = 0 Reorder the terms: 4x + -15x2 + 3x3 = 0 Solving 4x + -15x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -15x + 3x2) = 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 '(4 + -15x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + -15x + 3x2 = 0 Solving 4 + -15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -5x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -5x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -5x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -1.333333333 -5x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -5x + x2 = -1.333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1.333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1.333333333 + 6.25 Combine like terms: -1.333333333 + 6.25 = 4.916666667 6.25 + -5x + x2 = 4.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (x + -2.5) equal to 2.217355783 and -2.217355783.Subproblem 1
x + -2.5 = 2.217355783 Simplifying x + -2.5 = 2.217355783 Reorder the terms: -2.5 + x = 2.217355783 Solving -2.5 + x = 2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.217355783 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.217355783 + 2.5 x = 2.217355783 + 2.5 Combine like terms: 2.217355783 + 2.5 = 4.717355783 x = 4.717355783 Simplifying x = 4.717355783Subproblem 2
x + -2.5 = -2.217355783 Simplifying x + -2.5 = -2.217355783 Reorder the terms: -2.5 + x = -2.217355783 Solving -2.5 + x = -2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.217355783 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.217355783 + 2.5 x = -2.217355783 + 2.5 Combine like terms: -2.217355783 + 2.5 = 0.282644217 x = 0.282644217 Simplifying x = 0.282644217Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.717355783, 0.282644217}Solution
x = {0, 4.717355783, 0.282644217}
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