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Simplifying x3 = 11x + -3x2 Solving x3 = 11x + -3x2 Solving for variable 'x'. Reorder the terms: -11x + 3x2 + x3 = 11x + -3x2 + -11x + 3x2 Reorder the terms: -11x + 3x2 + x3 = 11x + -11x + -3x2 + 3x2 Combine like terms: 11x + -11x = 0 -11x + 3x2 + x3 = 0 + -3x2 + 3x2 -11x + 3x2 + x3 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -11x + 3x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 3x + 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 '(-11 + 3x + x2)' equal to zero and attempt to solve: Simplifying -11 + 3x + x2 = 0 Solving -11 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 3x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 3x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3x + x2 = 0 + 11 3x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 3x + x2 = 11 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 11 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 11 + 2.25 Combine like terms: 11 + 2.25 = 13.25 2.25 + 3x + x2 = 13.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 1.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + 1.5 = 3.640054945 Simplifying x + 1.5 = 3.640054945 Reorder the terms: 1.5 + x = 3.640054945 Solving 1.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.640054945 + -1.5 x = 3.640054945 + -1.5 Combine like terms: 3.640054945 + -1.5 = 2.140054945 x = 2.140054945 Simplifying x = 2.140054945Subproblem 2
x + 1.5 = -3.640054945 Simplifying x + 1.5 = -3.640054945 Reorder the terms: 1.5 + x = -3.640054945 Solving 1.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.640054945 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.640054945 + -1.5 x = -3.640054945 + -1.5 Combine like terms: -3.640054945 + -1.5 = -5.140054945 x = -5.140054945 Simplifying x = -5.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.140054945, -5.140054945}Solution
x = {0, 2.140054945, -5.140054945}
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