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Simplifying 13x2 + 3x + -2 = 0 Reorder the terms: -2 + 3x + 13x2 = 0 Solving -2 + 3x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.1538461538 + 0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + 0.2307692308x + 0.1538461538 + x2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + 0.2307692308x + x2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + 0.2307692308x + x2 = 0 + 0.1538461538 0.2307692308x + x2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 0.2307692308x + x2 = 0.1538461538 The x term is 0.2307692308x. Take half its coefficient (0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. 0.2307692308x + 0.01331360947 + x2 = 0.1538461538 + 0.01331360947 Reorder the terms: 0.01331360947 + 0.2307692308x + x2 = 0.1538461538 + 0.01331360947 Combine like terms: 0.1538461538 + 0.01331360947 = 0.16715976327 0.01331360947 + 0.2307692308x + x2 = 0.16715976327 Factor a perfect square on the left side: (x + 0.1153846154)(x + 0.1153846154) = 0.16715976327 Calculate the square root of the right side: 0.408851762 Break this problem into two subproblems by setting (x + 0.1153846154) equal to 0.408851762 and -0.408851762.Subproblem 1
x + 0.1153846154 = 0.408851762 Simplifying x + 0.1153846154 = 0.408851762 Reorder the terms: 0.1153846154 + x = 0.408851762 Solving 0.1153846154 + x = 0.408851762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 0.408851762 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 0.408851762 + -0.1153846154 x = 0.408851762 + -0.1153846154 Combine like terms: 0.408851762 + -0.1153846154 = 0.2934671466 x = 0.2934671466 Simplifying x = 0.2934671466Subproblem 2
x + 0.1153846154 = -0.408851762 Simplifying x + 0.1153846154 = -0.408851762 Reorder the terms: 0.1153846154 + x = -0.408851762 Solving 0.1153846154 + x = -0.408851762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -0.408851762 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -0.408851762 + -0.1153846154 x = -0.408851762 + -0.1153846154 Combine like terms: -0.408851762 + -0.1153846154 = -0.5242363774 x = -0.5242363774 Simplifying x = -0.5242363774Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2934671466, -0.5242363774}
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