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Simplifying 94 = 8w + 5w2 Solving 94 = 8w + 5w2 Solving for variable 'w'. Reorder the terms: 94 + -8w + -5w2 = 8w + -8w + 5w2 + -5w2 Combine like terms: 8w + -8w = 0 94 + -8w + -5w2 = 0 + 5w2 + -5w2 94 + -8w + -5w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 94 + -8w + -5w2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -18.8 + 1.6w + w2 = 0 Move the constant term to the right: Add '18.8' to each side of the equation. -18.8 + 1.6w + 18.8 + w2 = 0 + 18.8 Reorder the terms: -18.8 + 18.8 + 1.6w + w2 = 0 + 18.8 Combine like terms: -18.8 + 18.8 = 0.0 0.0 + 1.6w + w2 = 0 + 18.8 1.6w + w2 = 0 + 18.8 Combine like terms: 0 + 18.8 = 18.8 1.6w + w2 = 18.8 The w term is 1.6w. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6w + 0.64 + w2 = 18.8 + 0.64 Reorder the terms: 0.64 + 1.6w + w2 = 18.8 + 0.64 Combine like terms: 18.8 + 0.64 = 19.44 0.64 + 1.6w + w2 = 19.44 Factor a perfect square on the left side: (w + 0.8)(w + 0.8) = 19.44 Calculate the square root of the right side: 4.409081537 Break this problem into two subproblems by setting (w + 0.8) equal to 4.409081537 and -4.409081537.Subproblem 1
w + 0.8 = 4.409081537 Simplifying w + 0.8 = 4.409081537 Reorder the terms: 0.8 + w = 4.409081537 Solving 0.8 + w = 4.409081537 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + w = 4.409081537 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + w = 4.409081537 + -0.8 w = 4.409081537 + -0.8 Combine like terms: 4.409081537 + -0.8 = 3.609081537 w = 3.609081537 Simplifying w = 3.609081537Subproblem 2
w + 0.8 = -4.409081537 Simplifying w + 0.8 = -4.409081537 Reorder the terms: 0.8 + w = -4.409081537 Solving 0.8 + w = -4.409081537 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + w = -4.409081537 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + w = -4.409081537 + -0.8 w = -4.409081537 + -0.8 Combine like terms: -4.409081537 + -0.8 = -5.209081537 w = -5.209081537 Simplifying w = -5.209081537Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.609081537, -5.209081537}
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