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Simplifying x3 + 5x2 + -10x = 0 Reorder the terms: -10x + 5x2 + x3 = 0 Solving -10x + 5x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + 5x + 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 '(-10 + 5x + x2)' equal to zero and attempt to solve: Simplifying -10 + 5x + x2 = 0 Solving -10 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 5x + x2 = 0 + 10 5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 5x + x2 = 10 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 = 10 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 10 + 6.25 Combine like terms: 10 + 6.25 = 16.25 6.25 + 5x + x2 = 16.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 2.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 2.5 = 4.031128874 Simplifying x + 2.5 = 4.031128874 Reorder the terms: 2.5 + x = 4.031128874 Solving 2.5 + x = 4.031128874 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 = 4.031128874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.031128874 + -2.5 x = 4.031128874 + -2.5 Combine like terms: 4.031128874 + -2.5 = 1.531128874 x = 1.531128874 Simplifying x = 1.531128874Subproblem 2
x + 2.5 = -4.031128874 Simplifying x + 2.5 = -4.031128874 Reorder the terms: 2.5 + x = -4.031128874 Solving 2.5 + x = -4.031128874 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 = -4.031128874 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.031128874 + -2.5 x = -4.031128874 + -2.5 Combine like terms: -4.031128874 + -2.5 = -6.531128874 x = -6.531128874 Simplifying x = -6.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.531128874, -6.531128874}Solution
x = {0, 1.531128874, -6.531128874}
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