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Simplifying 75w2 + 35w + 3 = 0 Reorder the terms: 3 + 35w + 75w2 = 0 Solving 3 + 35w + 75w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.04 + 0.4666666667w + w2 = 0 Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 0.4666666667w + -0.04 + w2 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 0.4666666667w + w2 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 0.4666666667w + w2 = 0 + -0.04 0.4666666667w + w2 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 0.4666666667w + w2 = -0.04 The w term is 0.4666666667w. Take half its coefficient (0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. 0.4666666667w + 0.05444444448 + w2 = -0.04 + 0.05444444448 Reorder the terms: 0.05444444448 + 0.4666666667w + w2 = -0.04 + 0.05444444448 Combine like terms: -0.04 + 0.05444444448 = 0.01444444448 0.05444444448 + 0.4666666667w + w2 = 0.01444444448 Factor a perfect square on the left side: (w + 0.2333333334)(w + 0.2333333334) = 0.01444444448 Calculate the square root of the right side: 0.120185043 Break this problem into two subproblems by setting (w + 0.2333333334) equal to 0.120185043 and -0.120185043.Subproblem 1
w + 0.2333333334 = 0.120185043 Simplifying w + 0.2333333334 = 0.120185043 Reorder the terms: 0.2333333334 + w = 0.120185043 Solving 0.2333333334 + w = 0.120185043 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + w = 0.120185043 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + w = 0.120185043 + -0.2333333334 w = 0.120185043 + -0.2333333334 Combine like terms: 0.120185043 + -0.2333333334 = -0.1131482904 w = -0.1131482904 Simplifying w = -0.1131482904Subproblem 2
w + 0.2333333334 = -0.120185043 Simplifying w + 0.2333333334 = -0.120185043 Reorder the terms: 0.2333333334 + w = -0.120185043 Solving 0.2333333334 + w = -0.120185043 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2333333334' to each side of the equation. 0.2333333334 + -0.2333333334 + w = -0.120185043 + -0.2333333334 Combine like terms: 0.2333333334 + -0.2333333334 = 0.0000000000 0.0000000000 + w = -0.120185043 + -0.2333333334 w = -0.120185043 + -0.2333333334 Combine like terms: -0.120185043 + -0.2333333334 = -0.3535183764 w = -0.3535183764 Simplifying w = -0.3535183764Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.1131482904, -0.3535183764}
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