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Simplifying 2x3 + -13x2 + -6x = 0 Reorder the terms: -6x + -13x2 + 2x3 = 0 Solving -6x + -13x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -13x + 2x2) = 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 + -13x + 2x2)' equal to zero and attempt to solve: Simplifying -6 + -13x + 2x2 = 0 Solving -6 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + -6.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6.5x + x2 = 0 + 3 -6.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6.5x + x2 = 3 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 3 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 3 + 10.5625 Combine like terms: 3 + 10.5625 = 13.5625 10.5625 + -6.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + -3.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + -3.25 = 3.682729966 Simplifying x + -3.25 = 3.682729966 Reorder the terms: -3.25 + x = 3.682729966 Solving -3.25 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 3.682729966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 3.682729966 + 3.25 x = 3.682729966 + 3.25 Combine like terms: 3.682729966 + 3.25 = 6.932729966 x = 6.932729966 Simplifying x = 6.932729966Subproblem 2
x + -3.25 = -3.682729966 Simplifying x + -3.25 = -3.682729966 Reorder the terms: -3.25 + x = -3.682729966 Solving -3.25 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -3.682729966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -3.682729966 + 3.25 x = -3.682729966 + 3.25 Combine like terms: -3.682729966 + 3.25 = -0.432729966 x = -0.432729966 Simplifying x = -0.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.932729966, -0.432729966}Solution
x = {0, 6.932729966, -0.432729966}
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