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Simplifying 0 = 13x2 + -1x + -2 Reorder the terms: 0 = -2 + -1x + 13x2 Solving 0 = -2 + -1x + 13x2 Solving for variable 'x'. Combine like terms: 0 + 2 = 2 2 + x + -13x2 = -2 + -1x + 13x2 + 2 + x + -13x2 Reorder the terms: 2 + x + -13x2 = -2 + 2 + -1x + x + 13x2 + -13x2 Combine like terms: -2 + 2 = 0 2 + x + -13x2 = 0 + -1x + x + 13x2 + -13x2 2 + x + -13x2 = -1x + x + 13x2 + -13x2 Combine like terms: -1x + x = 0 2 + x + -13x2 = 0 + 13x2 + -13x2 2 + x + -13x2 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 2 + x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.1538461538 + -0.07692307692x + x2 = 0 Move the constant term to the right: Add '0.1538461538' to each side of the equation. -0.1538461538 + -0.07692307692x + 0.1538461538 + x2 = 0 + 0.1538461538 Reorder the terms: -0.1538461538 + 0.1538461538 + -0.07692307692x + x2 = 0 + 0.1538461538 Combine like terms: -0.1538461538 + 0.1538461538 = 0.0000000000 0.0000000000 + -0.07692307692x + x2 = 0 + 0.1538461538 -0.07692307692x + x2 = 0 + 0.1538461538 Combine like terms: 0 + 0.1538461538 = 0.1538461538 -0.07692307692x + x2 = 0.1538461538 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. -0.07692307692x + 0.25 + x2 = 0.1538461538 + 0.25 Reorder the terms: 0.25 + -0.07692307692x + x2 = 0.1538461538 + 0.25 Combine like terms: 0.1538461538 + 0.25 = 0.4038461538 0.25 + -0.07692307692x + x2 = 0.4038461538 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4038461538 Calculate the square root of the right side: 0.635488909 Break this problem into two subproblems by setting (x + 0.5) equal to 0.635488909 and -0.635488909.Subproblem 1
x + 0.5 = 0.635488909 Simplifying x + 0.5 = 0.635488909 Reorder the terms: 0.5 + x = 0.635488909 Solving 0.5 + x = 0.635488909 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 = 0.635488909 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.635488909 + -0.5 x = 0.635488909 + -0.5 Combine like terms: 0.635488909 + -0.5 = 0.135488909 x = 0.135488909 Simplifying x = 0.135488909Subproblem 2
x + 0.5 = -0.635488909 Simplifying x + 0.5 = -0.635488909 Reorder the terms: 0.5 + x = -0.635488909 Solving 0.5 + x = -0.635488909 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 = -0.635488909 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.635488909 + -0.5 x = -0.635488909 + -0.5 Combine like terms: -0.635488909 + -0.5 = -1.135488909 x = -1.135488909 Simplifying x = -1.135488909Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.135488909, -1.135488909}
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