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Simplifying (-7w2 + -2w + -1) + -1(5w2 + 3w + -2) = 0 Reorder the terms: (-1 + -2w + -7w2) + -1(5w2 + 3w + -2) = 0 Remove parenthesis around (-1 + -2w + -7w2) -1 + -2w + -7w2 + -1(5w2 + 3w + -2) = 0 Reorder the terms: -1 + -2w + -7w2 + -1(-2 + 3w + 5w2) = 0 -1 + -2w + -7w2 + (-2 * -1 + 3w * -1 + 5w2 * -1) = 0 -1 + -2w + -7w2 + (2 + -3w + -5w2) = 0 Reorder the terms: -1 + 2 + -2w + -3w + -7w2 + -5w2 = 0 Combine like terms: -1 + 2 = 1 1 + -2w + -3w + -7w2 + -5w2 = 0 Combine like terms: -2w + -3w = -5w 1 + -5w + -7w2 + -5w2 = 0 Combine like terms: -7w2 + -5w2 = -12w2 1 + -5w + -12w2 = 0 Solving 1 + -5w + -12w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + 0.4166666667w + w2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.4166666667w + 0.08333333333 + w2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.4166666667w + w2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.4166666667w + w2 = 0 + 0.08333333333 0.4166666667w + w2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.4166666667w + w2 = 0.08333333333 The w term is 0.4166666667w. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667w + 0.04340277781 + w2 = 0.08333333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667w + w2 = 0.08333333333 + 0.04340277781 Combine like terms: 0.08333333333 + 0.04340277781 = 0.12673611114 0.04340277781 + 0.4166666667w + w2 = 0.12673611114 Factor a perfect square on the left side: (w + 0.2083333334)(w + 0.2083333334) = 0.12673611114 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (w + 0.2083333334) equal to 0.356000156 and -0.356000156.Subproblem 1
w + 0.2083333334 = 0.356000156 Simplifying w + 0.2083333334 = 0.356000156 Reorder the terms: 0.2083333334 + w = 0.356000156 Solving 0.2083333334 + w = 0.356000156 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + w = 0.356000156 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + w = 0.356000156 + -0.2083333334 w = 0.356000156 + -0.2083333334 Combine like terms: 0.356000156 + -0.2083333334 = 0.1476668226 w = 0.1476668226 Simplifying w = 0.1476668226Subproblem 2
w + 0.2083333334 = -0.356000156 Simplifying w + 0.2083333334 = -0.356000156 Reorder the terms: 0.2083333334 + w = -0.356000156 Solving 0.2083333334 + w = -0.356000156 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + w = -0.356000156 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + w = -0.356000156 + -0.2083333334 w = -0.356000156 + -0.2083333334 Combine like terms: -0.356000156 + -0.2083333334 = -0.5643334894 w = -0.5643334894 Simplifying w = -0.5643334894Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.1476668226, -0.5643334894}
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