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Simplifying 13x2 + -2x + -8 = 0 Reorder the terms: -8 + -2x + 13x2 = 0 Solving -8 + -2x + 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'. -0.6153846154 + -0.1538461538x + x2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + -0.1538461538x + 0.6153846154 + x2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + -0.1538461538x + x2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + -0.1538461538x + x2 = 0 + 0.6153846154 -0.1538461538x + x2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 -0.1538461538x + x2 = 0.6153846154 The x term is -0.1538461538x. Take half its coefficient (-0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. -0.1538461538x + 0.005917159760 + x2 = 0.6153846154 + 0.005917159760 Reorder the terms: 0.005917159760 + -0.1538461538x + x2 = 0.6153846154 + 0.005917159760 Combine like terms: 0.6153846154 + 0.005917159760 = 0.62130177516 0.005917159760 + -0.1538461538x + x2 = 0.62130177516 Factor a perfect square on the left side: (x + -0.0769230769)(x + -0.0769230769) = 0.62130177516 Calculate the square root of the right side: 0.788226982 Break this problem into two subproblems by setting (x + -0.0769230769) equal to 0.788226982 and -0.788226982.Subproblem 1
x + -0.0769230769 = 0.788226982 Simplifying x + -0.0769230769 = 0.788226982 Reorder the terms: -0.0769230769 + x = 0.788226982 Solving -0.0769230769 + x = 0.788226982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0769230769' to each side of the equation. -0.0769230769 + 0.0769230769 + x = 0.788226982 + 0.0769230769 Combine like terms: -0.0769230769 + 0.0769230769 = 0.0000000000 0.0000000000 + x = 0.788226982 + 0.0769230769 x = 0.788226982 + 0.0769230769 Combine like terms: 0.788226982 + 0.0769230769 = 0.8651500589 x = 0.8651500589 Simplifying x = 0.8651500589Subproblem 2
x + -0.0769230769 = -0.788226982 Simplifying x + -0.0769230769 = -0.788226982 Reorder the terms: -0.0769230769 + x = -0.788226982 Solving -0.0769230769 + x = -0.788226982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0769230769' to each side of the equation. -0.0769230769 + 0.0769230769 + x = -0.788226982 + 0.0769230769 Combine like terms: -0.0769230769 + 0.0769230769 = 0.0000000000 0.0000000000 + x = -0.788226982 + 0.0769230769 x = -0.788226982 + 0.0769230769 Combine like terms: -0.788226982 + 0.0769230769 = -0.7113039051 x = -0.7113039051 Simplifying x = -0.7113039051Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8651500589, -0.7113039051}
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