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Simplifying 13x2 + 8x + -22 = 0 Reorder the terms: -22 + 8x + 13x2 = 0 Solving -22 + 8x + 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 + 0.6153846154x + x2 = 0 Move the constant term to the right: Add '1.692307692' to each side of the equation. -1.692307692 + 0.6153846154x + 1.692307692 + x2 = 0 + 1.692307692 Reorder the terms: -1.692307692 + 1.692307692 + 0.6153846154x + x2 = 0 + 1.692307692 Combine like terms: -1.692307692 + 1.692307692 = 0.000000000 0.000000000 + 0.6153846154x + x2 = 0 + 1.692307692 0.6153846154x + x2 = 0 + 1.692307692 Combine like terms: 0 + 1.692307692 = 1.692307692 0.6153846154x + x2 = 1.692307692 The x term is 0.6153846154x. Take half its coefficient (0.3076923077). Square it (0.09467455622) and add it to both sides. Add '0.09467455622' to each side of the equation. 0.6153846154x + 0.09467455622 + x2 = 1.692307692 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154x + x2 = 1.692307692 + 0.09467455622 Combine like terms: 1.692307692 + 0.09467455622 = 1.78698224822 0.09467455622 + 0.6153846154x + x2 = 1.78698224822 Factor a perfect square on the left side: (x + 0.3076923077)(x + 0.3076923077) = 1.78698224822 Calculate the square root of the right side: 1.336780554 Break this problem into two subproblems by setting (x + 0.3076923077) equal to 1.336780554 and -1.336780554.Subproblem 1
x + 0.3076923077 = 1.336780554 Simplifying x + 0.3076923077 = 1.336780554 Reorder the terms: 0.3076923077 + x = 1.336780554 Solving 0.3076923077 + x = 1.336780554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = 1.336780554 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = 1.336780554 + -0.3076923077 x = 1.336780554 + -0.3076923077 Combine like terms: 1.336780554 + -0.3076923077 = 1.0290882463 x = 1.0290882463 Simplifying x = 1.0290882463Subproblem 2
x + 0.3076923077 = -1.336780554 Simplifying x + 0.3076923077 = -1.336780554 Reorder the terms: 0.3076923077 + x = -1.336780554 Solving 0.3076923077 + x = -1.336780554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + x = -1.336780554 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + x = -1.336780554 + -0.3076923077 x = -1.336780554 + -0.3076923077 Combine like terms: -1.336780554 + -0.3076923077 = -1.6444728617 x = -1.6444728617 Simplifying x = -1.6444728617Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0290882463, -1.6444728617}
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