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Simplifying 2w2 + -30w = -60 Reorder the terms: -30w + 2w2 = -60 Solving -30w + 2w2 = -60 Solving for variable 'w'. Reorder the terms: 60 + -30w + 2w2 = -60 + 60 Combine like terms: -60 + 60 = 0 60 + -30w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -15w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -15w + w2)' equal to zero and attempt to solve: Simplifying 30 + -15w + w2 = 0 Solving 30 + -15w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -15w + -30 + w2 = 0 + -30 Reorder the terms: 30 + -30 + -15w + w2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -15w + w2 = 0 + -30 -15w + w2 = 0 + -30 Combine like terms: 0 + -30 = -30 -15w + w2 = -30 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 = -30 + 56.25 Reorder the terms: 56.25 + -15w + w2 = -30 + 56.25 Combine like terms: -30 + 56.25 = 26.25 56.25 + -15w + w2 = 26.25 Factor a perfect square on the left side: (w + -7.5)(w + -7.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (w + -7.5) equal to 5.123475383 and -5.123475383.Subproblem 1
w + -7.5 = 5.123475383 Simplifying w + -7.5 = 5.123475383 Reorder the terms: -7.5 + w = 5.123475383 Solving -7.5 + w = 5.123475383 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 = 5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = 5.123475383 + 7.5 w = 5.123475383 + 7.5 Combine like terms: 5.123475383 + 7.5 = 12.623475383 w = 12.623475383 Simplifying w = 12.623475383Subproblem 2
w + -7.5 = -5.123475383 Simplifying w + -7.5 = -5.123475383 Reorder the terms: -7.5 + w = -5.123475383 Solving -7.5 + w = -5.123475383 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 = -5.123475383 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + w = -5.123475383 + 7.5 w = -5.123475383 + 7.5 Combine like terms: -5.123475383 + 7.5 = 2.376524617 w = 2.376524617 Simplifying w = 2.376524617Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.623475383, 2.376524617}Solution
w = {12.623475383, 2.376524617}
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