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Simplifying 36x3 + 13x2 + -1x = 0 Reorder the terms: -1x + 13x2 + 36x3 = 0 Solving -1x + 13x2 + 36x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + 13x + 36x2) = 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 '(-1 + 13x + 36x2)' equal to zero and attempt to solve: Simplifying -1 + 13x + 36x2 = 0 Solving -1 + 13x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + 0.3611111111x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.3611111111x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + 0.3611111111x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + 0.3611111111x + x2 = 0 + 0.02777777778 0.3611111111x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 0.3611111111x + x2 = 0.02777777778 The x term is 0.3611111111x. Take half its coefficient (0.1805555556). Square it (0.03260030866) and add it to both sides. Add '0.03260030866' to each side of the equation. 0.3611111111x + 0.03260030866 + x2 = 0.02777777778 + 0.03260030866 Reorder the terms: 0.03260030866 + 0.3611111111x + x2 = 0.02777777778 + 0.03260030866 Combine like terms: 0.02777777778 + 0.03260030866 = 0.06037808644 0.03260030866 + 0.3611111111x + x2 = 0.06037808644 Factor a perfect square on the left side: (x + 0.1805555556)(x + 0.1805555556) = 0.06037808644 Calculate the square root of the right side: 0.245719528 Break this problem into two subproblems by setting (x + 0.1805555556) equal to 0.245719528 and -0.245719528.Subproblem 1
x + 0.1805555556 = 0.245719528 Simplifying x + 0.1805555556 = 0.245719528 Reorder the terms: 0.1805555556 + x = 0.245719528 Solving 0.1805555556 + x = 0.245719528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1805555556' to each side of the equation. 0.1805555556 + -0.1805555556 + x = 0.245719528 + -0.1805555556 Combine like terms: 0.1805555556 + -0.1805555556 = 0.0000000000 0.0000000000 + x = 0.245719528 + -0.1805555556 x = 0.245719528 + -0.1805555556 Combine like terms: 0.245719528 + -0.1805555556 = 0.0651639724 x = 0.0651639724 Simplifying x = 0.0651639724Subproblem 2
x + 0.1805555556 = -0.245719528 Simplifying x + 0.1805555556 = -0.245719528 Reorder the terms: 0.1805555556 + x = -0.245719528 Solving 0.1805555556 + x = -0.245719528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1805555556' to each side of the equation. 0.1805555556 + -0.1805555556 + x = -0.245719528 + -0.1805555556 Combine like terms: 0.1805555556 + -0.1805555556 = 0.0000000000 0.0000000000 + x = -0.245719528 + -0.1805555556 x = -0.245719528 + -0.1805555556 Combine like terms: -0.245719528 + -0.1805555556 = -0.4262750836 x = -0.4262750836 Simplifying x = -0.4262750836Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0651639724, -0.4262750836}Solution
x = {0, 0.0651639724, -0.4262750836}
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