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Simplifying x3 + -10x2 + -13x = 0 Reorder the terms: -13x + -10x2 + x3 = 0 Solving -13x + -10x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + -10x + 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 '(-13 + -10x + x2)' equal to zero and attempt to solve: Simplifying -13 + -10x + x2 = 0 Solving -13 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -10x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -10x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -10x + x2 = 0 + 13 -10x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -10x + x2 = 13 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 13 + 25 Reorder the terms: 25 + -10x + x2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + -10x + x2 = 38 Factor a perfect square on the left side: (x + -5)(x + -5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -5) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -5 = 6.164414003 Simplifying x + -5 = 6.164414003 Reorder the terms: -5 + x = 6.164414003 Solving -5 + x = 6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.164414003 + 5 x = 6.164414003 + 5 Combine like terms: 6.164414003 + 5 = 11.164414003 x = 11.164414003 Simplifying x = 11.164414003Subproblem 2
x + -5 = -6.164414003 Simplifying x + -5 = -6.164414003 Reorder the terms: -5 + x = -6.164414003 Solving -5 + x = -6.164414003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.164414003 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.164414003 + 5 x = -6.164414003 + 5 Combine like terms: -6.164414003 + 5 = -1.164414003 x = -1.164414003 Simplifying x = -1.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.164414003, -1.164414003}Solution
x = {0, 11.164414003, -1.164414003}
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