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Simplifying 13x2 + 21x + -22 = 0 Reorder the terms: -22 + 21x + 13x2 = 0 Solving -22 + 21x + 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'. -1.692307692 + 1.615384615x + x2 = 0 Move the constant term to the right: Add '1.692307692' to each side of the equation. -1.692307692 + 1.615384615x + 1.692307692 + x2 = 0 + 1.692307692 Reorder the terms: -1.692307692 + 1.692307692 + 1.615384615x + x2 = 0 + 1.692307692 Combine like terms: -1.692307692 + 1.692307692 = 0.000000000 0.000000000 + 1.615384615x + x2 = 0 + 1.692307692 1.615384615x + x2 = 0 + 1.692307692 Combine like terms: 0 + 1.692307692 = 1.692307692 1.615384615x + x2 = 1.692307692 The x term is 1.615384615x. Take half its coefficient (0.8076923075). Square it (0.6523668636) and add it to both sides. Add '0.6523668636' to each side of the equation. 1.615384615x + 0.6523668636 + x2 = 1.692307692 + 0.6523668636 Reorder the terms: 0.6523668636 + 1.615384615x + x2 = 1.692307692 + 0.6523668636 Combine like terms: 1.692307692 + 0.6523668636 = 2.3446745556 0.6523668636 + 1.615384615x + x2 = 2.3446745556 Factor a perfect square on the left side: (x + 0.8076923075)(x + 0.8076923075) = 2.3446745556 Calculate the square root of the right side: 1.531233018 Break this problem into two subproblems by setting (x + 0.8076923075) equal to 1.531233018 and -1.531233018.Subproblem 1
x + 0.8076923075 = 1.531233018 Simplifying x + 0.8076923075 = 1.531233018 Reorder the terms: 0.8076923075 + x = 1.531233018 Solving 0.8076923075 + x = 1.531233018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8076923075' to each side of the equation. 0.8076923075 + -0.8076923075 + x = 1.531233018 + -0.8076923075 Combine like terms: 0.8076923075 + -0.8076923075 = 0.0000000000 0.0000000000 + x = 1.531233018 + -0.8076923075 x = 1.531233018 + -0.8076923075 Combine like terms: 1.531233018 + -0.8076923075 = 0.7235407105 x = 0.7235407105 Simplifying x = 0.7235407105Subproblem 2
x + 0.8076923075 = -1.531233018 Simplifying x + 0.8076923075 = -1.531233018 Reorder the terms: 0.8076923075 + x = -1.531233018 Solving 0.8076923075 + x = -1.531233018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8076923075' to each side of the equation. 0.8076923075 + -0.8076923075 + x = -1.531233018 + -0.8076923075 Combine like terms: 0.8076923075 + -0.8076923075 = 0.0000000000 0.0000000000 + x = -1.531233018 + -0.8076923075 x = -1.531233018 + -0.8076923075 Combine like terms: -1.531233018 + -0.8076923075 = -2.3389253255 x = -2.3389253255 Simplifying x = -2.3389253255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7235407105, -2.3389253255}
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