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Simplifying 2x3 + x2 + -16x + -10x = 0 Reorder the terms: -16x + -10x + x2 + 2x3 = 0 Combine like terms: -16x + -10x = -26x -26x + x2 + 2x3 = 0 Solving -26x + x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-26 + 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 '(-26 + x + 2x2)' equal to zero and attempt to solve: Simplifying -26 + x + 2x2 = 0 Solving -26 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + 0.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 0.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 0.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 0.5x + x2 = 0 + 13 0.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 0.5x + x2 = 13 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 = 13 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + 0.5x + x2 = 13.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + 0.5 = 3.640054945 Simplifying x + 0.5 = 3.640054945 Reorder the terms: 0.5 + x = 3.640054945 Solving 0.5 + x = 3.640054945 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 = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.640054945 + -0.5 x = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 x = 3.140054945 Simplifying x = 3.140054945Subproblem 2
x + 0.5 = -3.640054945 Simplifying x + 0.5 = -3.640054945 Reorder the terms: 0.5 + x = -3.640054945 Solving 0.5 + x = -3.640054945 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 = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.640054945 + -0.5 x = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 x = -4.140054945 Simplifying x = -4.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.140054945, -4.140054945}Solution
x = {0, 3.140054945, -4.140054945}
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