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Simplifying 60w + 40w2 = 175 Solving 60w + 40w2 = 175 Solving for variable 'w'. Reorder the terms: -175 + 60w + 40w2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 60w + 40w2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-35 + 12w + 8w2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-35 + 12w + 8w2)' equal to zero and attempt to solve: Simplifying -35 + 12w + 8w2 = 0 Solving -35 + 12w + 8w2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.375 + 1.5w + w2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 1.5w + 4.375 + w2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 1.5w + w2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 1.5w + w2 = 0 + 4.375 1.5w + w2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 1.5w + w2 = 4.375 The w term is 1.5w. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5w + 0.5625 + w2 = 4.375 + 0.5625 Reorder the terms: 0.5625 + 1.5w + w2 = 4.375 + 0.5625 Combine like terms: 4.375 + 0.5625 = 4.9375 0.5625 + 1.5w + w2 = 4.9375 Factor a perfect square on the left side: (w + 0.75)(w + 0.75) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (w + 0.75) equal to 2.222048604 and -2.222048604.Subproblem 1
w + 0.75 = 2.222048604 Simplifying w + 0.75 = 2.222048604 Reorder the terms: 0.75 + w = 2.222048604 Solving 0.75 + w = 2.222048604 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = 2.222048604 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = 2.222048604 + -0.75 w = 2.222048604 + -0.75 Combine like terms: 2.222048604 + -0.75 = 1.472048604 w = 1.472048604 Simplifying w = 1.472048604Subproblem 2
w + 0.75 = -2.222048604 Simplifying w + 0.75 = -2.222048604 Reorder the terms: 0.75 + w = -2.222048604 Solving 0.75 + w = -2.222048604 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = -2.222048604 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = -2.222048604 + -0.75 w = -2.222048604 + -0.75 Combine like terms: -2.222048604 + -0.75 = -2.972048604 w = -2.972048604 Simplifying w = -2.972048604Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.472048604, -2.972048604}Solution
w = {1.472048604, -2.972048604}
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