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Simplifying 13x2 + -3x + -6 = 0 Reorder the terms: -6 + -3x + 13x2 = 0 Solving -6 + -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'. -0.4615384615 + -0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + -0.2307692308x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + -0.2307692308x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + -0.2307692308x + x2 = 0 + 0.4615384615 -0.2307692308x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 -0.2307692308x + x2 = 0.4615384615 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 = 0.4615384615 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308x + x2 = 0.4615384615 + 0.01331360947 Combine like terms: 0.4615384615 + 0.01331360947 = 0.47485207097 0.01331360947 + -0.2307692308x + x2 = 0.47485207097 Factor a perfect square on the left side: (x + -0.1153846154)(x + -0.1153846154) = 0.47485207097 Calculate the square root of the right side: 0.68909511 Break this problem into two subproblems by setting (x + -0.1153846154) equal to 0.68909511 and -0.68909511.Subproblem 1
x + -0.1153846154 = 0.68909511 Simplifying x + -0.1153846154 = 0.68909511 Reorder the terms: -0.1153846154 + x = 0.68909511 Solving -0.1153846154 + x = 0.68909511 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 = 0.68909511 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = 0.68909511 + 0.1153846154 x = 0.68909511 + 0.1153846154 Combine like terms: 0.68909511 + 0.1153846154 = 0.8044797254 x = 0.8044797254 Simplifying x = 0.8044797254Subproblem 2
x + -0.1153846154 = -0.68909511 Simplifying x + -0.1153846154 = -0.68909511 Reorder the terms: -0.1153846154 + x = -0.68909511 Solving -0.1153846154 + x = -0.68909511 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 = -0.68909511 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + x = -0.68909511 + 0.1153846154 x = -0.68909511 + 0.1153846154 Combine like terms: -0.68909511 + 0.1153846154 = -0.5737104946 x = -0.5737104946 Simplifying x = -0.5737104946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8044797254, -0.5737104946}
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