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Simplifying x3 + 15x2 + -6x = 0 Reorder the terms: -6x + 15x2 + x3 = 0 Solving -6x + 15x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 15x + x2) = 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 '(-6 + 15x + x2)' equal to zero and attempt to solve: Simplifying -6 + 15x + x2 = 0 Solving -6 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 15x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 15x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 15x + x2 = 0 + 6 15x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 15x + x2 = 6 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 6 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 6 + 56.25 Combine like terms: 6 + 56.25 = 62.25 56.25 + 15x + x2 = 62.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 7.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 7.5 = 7.889866919 Simplifying x + 7.5 = 7.889866919 Reorder the terms: 7.5 + x = 7.889866919 Solving 7.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.889866919 + -7.5 x = 7.889866919 + -7.5 Combine like terms: 7.889866919 + -7.5 = 0.389866919 x = 0.389866919 Simplifying x = 0.389866919Subproblem 2
x + 7.5 = -7.889866919 Simplifying x + 7.5 = -7.889866919 Reorder the terms: 7.5 + x = -7.889866919 Solving 7.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.889866919 + -7.5 x = -7.889866919 + -7.5 Combine like terms: -7.889866919 + -7.5 = -15.389866919 x = -15.389866919 Simplifying x = -15.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389866919, -15.389866919}Solution
x = {0, 0.389866919, -15.389866919}
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