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Simplifying 4w2 + -60w + 200 = 400 Reorder the terms: 200 + -60w + 4w2 = 400 Solving 200 + -60w + 4w2 = 400 Solving for variable 'w'. Reorder the terms: 200 + -400 + -60w + 4w2 = 400 + -400 Combine like terms: 200 + -400 = -200 -200 + -60w + 4w2 = 400 + -400 Combine like terms: 400 + -400 = 0 -200 + -60w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + -15w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + -15w + w2)' equal to zero and attempt to solve: Simplifying -50 + -15w + w2 = 0 Solving -50 + -15w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -15w + 50 + w2 = 0 + 50 Reorder the terms: -50 + 50 + -15w + w2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15w + w2 = 0 + 50 -15w + w2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15w + w2 = 50 The w term is -15w. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15w + 56.25 + w2 = 50 + 56.25 Reorder the terms: 56.25 + -15w + w2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15w + w2 = 106.25 Factor a perfect square on the left side: (w + -7.5)(w + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (w + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
w + -7.5 = 10.307764064 Simplifying w + -7.5 = 10.307764064 Reorder the terms: -7.5 + w = 10.307764064 Solving -7.5 + w = 10.307764064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + w = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = 10.307764064 + 7.5 w = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 w = 17.807764064 Simplifying w = 17.807764064Subproblem 2
w + -7.5 = -10.307764064 Simplifying w + -7.5 = -10.307764064 Reorder the terms: -7.5 + w = -10.307764064 Solving -7.5 + w = -10.307764064 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + w = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = -10.307764064 + 7.5 w = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 w = -2.807764064 Simplifying w = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. w = {17.807764064, -2.807764064}Solution
w = {17.807764064, -2.807764064}
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