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Simplifying 13x2 + -3x + -18 = 0 Reorder the terms: -18 + -3x + 13x2 = 0 Solving -18 + -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'. -1.384615385 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '1.384615385' to each side of the equation. -1.384615385 + -0.2307692308x + 1.384615385 + x2 = 0 + 1.384615385 Reorder the terms: -1.384615385 + 1.384615385 + -0.2307692308x + x2 = 0 + 1.384615385 Combine like terms: -1.384615385 + 1.384615385 = 0.000000000 0.000000000 + -0.2307692308x + x2 = 0 + 1.384615385 -0.2307692308x + x2 = 0 + 1.384615385 Combine like terms: 0 + 1.384615385 = 1.384615385 -0.2307692308x + x2 = 1.384615385 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 = 1.384615385 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 1.384615385 + 0.01331360947 Combine like terms: 1.384615385 + 0.01331360947 = 1.39792899447 0.01331360947 + -0.2307692308x + x2 = 1.39792899447 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 1.39792899447 Calculate the square root of the right side: 1.182340473 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 1.182340473 and -1.182340473.Subproblem 1
x + -0.1153846154 = 1.182340473 Simplifying x + -0.1153846154 = 1.182340473 Reorder the terms: -0.1153846154 + x = 1.182340473 Solving -0.1153846154 + x = 1.182340473 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 = 1.182340473 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 1.182340473 + 0.1153846154 x = 1.182340473 + 0.1153846154 Combine like terms: 1.182340473 + 0.1153846154 = 1.2977250884 x = 1.2977250884 Simplifying x = 1.2977250884Subproblem 2
x + -0.1153846154 = -1.182340473 Simplifying x + -0.1153846154 = -1.182340473 Reorder the terms: -0.1153846154 + x = -1.182340473 Solving -0.1153846154 + x = -1.182340473 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 = -1.182340473 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -1.182340473 + 0.1153846154 x = -1.182340473 + 0.1153846154 Combine like terms: -1.182340473 + 0.1153846154 = -1.0669558576 x = -1.0669558576 Simplifying x = -1.0669558576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2977250884, -1.0669558576}
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