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Simplifying 13w2 + 1 = -8w Reorder the terms: 1 + 13w2 = -8w Solving 1 + 13w2 = -8w Solving for variable 'w'. Reorder the terms: 1 + 8w + 13w2 = -8w + 8w Combine like terms: -8w + 8w = 0 1 + 8w + 13w2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.07692307692 + 0.6153846154w + w2 = 0 Move the constant term to the right: Add '-0.07692307692' to each side of the equation. 0.07692307692 + 0.6153846154w + -0.07692307692 + w2 = 0 + -0.07692307692 Reorder the terms: 0.07692307692 + -0.07692307692 + 0.6153846154w + w2 = 0 + -0.07692307692 Combine like terms: 0.07692307692 + -0.07692307692 = 0.00000000000 0.00000000000 + 0.6153846154w + w2 = 0 + -0.07692307692 0.6153846154w + w2 = 0 + -0.07692307692 Combine like terms: 0 + -0.07692307692 = -0.07692307692 0.6153846154w + w2 = -0.07692307692 The w term is 0.6153846154w. 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. 0.6153846154w + 0.09467455622 + w2 = -0.07692307692 + 0.09467455622 Reorder the terms: 0.09467455622 + 0.6153846154w + w2 = -0.07692307692 + 0.09467455622 Combine like terms: -0.07692307692 + 0.09467455622 = 0.0177514793 0.09467455622 + 0.6153846154w + w2 = 0.0177514793 Factor a perfect square on the left side: (w + 0.3076923077)(w + 0.3076923077) = 0.0177514793 Calculate the square root of the right side: 0.133234678 Break this problem into two subproblems by setting (w + 0.3076923077) equal to 0.133234678 and -0.133234678.Subproblem 1
w + 0.3076923077 = 0.133234678 Simplifying w + 0.3076923077 = 0.133234678 Reorder the terms: 0.3076923077 + w = 0.133234678 Solving 0.3076923077 + w = 0.133234678 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + w = 0.133234678 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + w = 0.133234678 + -0.3076923077 w = 0.133234678 + -0.3076923077 Combine like terms: 0.133234678 + -0.3076923077 = -0.1744576297 w = -0.1744576297 Simplifying w = -0.1744576297Subproblem 2
w + 0.3076923077 = -0.133234678 Simplifying w + 0.3076923077 = -0.133234678 Reorder the terms: 0.3076923077 + w = -0.133234678 Solving 0.3076923077 + w = -0.133234678 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3076923077' to each side of the equation. 0.3076923077 + -0.3076923077 + w = -0.133234678 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + w = -0.133234678 + -0.3076923077 w = -0.133234678 + -0.3076923077 Combine like terms: -0.133234678 + -0.3076923077 = -0.4409269857 w = -0.4409269857 Simplifying w = -0.4409269857Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.1744576297, -0.4409269857}
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