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Simplifying x3 + 2x2 + -13x = 0 Reorder the terms: -13x + 2x2 + x3 = 0 Solving -13x + 2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-13 + 2x + 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 + 2x + x2)' equal to zero and attempt to solve: Simplifying -13 + 2x + x2 = 0 Solving -13 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 2x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2x + x2 = 0 + 13 2x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 2x + x2 = 13 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 13 + 1 Reorder the terms: 1 + 2x + x2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2x + x2 = 14 Factor a perfect square on the left side: (x + 1)(x + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 1 = 3.741657387 Simplifying x + 1 = 3.741657387 Reorder the terms: 1 + x = 3.741657387 Solving 1 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.741657387 + -1 x = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 x = 2.741657387 Simplifying x = 2.741657387Subproblem 2
x + 1 = -3.741657387 Simplifying x + 1 = -3.741657387 Reorder the terms: 1 + x = -3.741657387 Solving 1 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.741657387 + -1 x = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 x = -4.741657387 Simplifying x = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.741657387, -4.741657387}Solution
x = {0, 2.741657387, -4.741657387}
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