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Simplifying 2x3 + x2 + -11x = 0 Reorder the terms: -11x + x2 + 2x3 = 0 Solving -11x + x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + x + 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 '(-11 + x + 2x2)' equal to zero and attempt to solve: Simplifying -11 + x + 2x2 = 0 Solving -11 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 0.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 0.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 0.5x + x2 = 0 + 5.5 0.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 0.5x + x2 = 5.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 5.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 5.5 + 0.25 Combine like terms: 5.5 + 0.25 = 5.75 0.25 + 0.5x + x2 = 5.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + 0.5) equal to 2.397915762 and -2.397915762.Subproblem 1
x + 0.5 = 2.397915762 Simplifying x + 0.5 = 2.397915762 Reorder the terms: 0.5 + x = 2.397915762 Solving 0.5 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.397915762 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.397915762 + -0.5 x = 2.397915762 + -0.5 Combine like terms: 2.397915762 + -0.5 = 1.897915762 x = 1.897915762 Simplifying x = 1.897915762Subproblem 2
x + 0.5 = -2.397915762 Simplifying x + 0.5 = -2.397915762 Reorder the terms: 0.5 + x = -2.397915762 Solving 0.5 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.397915762 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.397915762 + -0.5 x = -2.397915762 + -0.5 Combine like terms: -2.397915762 + -0.5 = -2.897915762 x = -2.897915762 Simplifying x = -2.897915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.897915762, -2.897915762}Solution
x = {0, 1.897915762, -2.897915762}
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