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Simplifying 0 = 12w2 + 30w + -4 Reorder the terms: 0 = -4 + 30w + 12w2 Solving 0 = -4 + 30w + 12w2 Solving for variable 'w'. Combine like terms: 0 + 4 = 4 4 + -30w + -12w2 = -4 + 30w + 12w2 + 4 + -30w + -12w2 Reorder the terms: 4 + -30w + -12w2 = -4 + 4 + 30w + -30w + 12w2 + -12w2 Combine like terms: -4 + 4 = 0 4 + -30w + -12w2 = 0 + 30w + -30w + 12w2 + -12w2 4 + -30w + -12w2 = 30w + -30w + 12w2 + -12w2 Combine like terms: 30w + -30w = 0 4 + -30w + -12w2 = 0 + 12w2 + -12w2 4 + -30w + -12w2 = 12w2 + -12w2 Combine like terms: 12w2 + -12w2 = 0 4 + -30w + -12w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -15w + -6w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -15w + -6w2)' equal to zero and attempt to solve: Simplifying 2 + -15w + -6w2 = 0 Solving 2 + -15w + -6w2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.3333333333 + 2.5w + w2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2.5w + 0.3333333333 + w2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2.5w + w2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2.5w + w2 = 0 + 0.3333333333 2.5w + w2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2.5w + w2 = 0.3333333333 The w term is 2.5w. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5w + 1.5625 + w2 = 0.3333333333 + 1.5625 Reorder the terms: 1.5625 + 2.5w + w2 = 0.3333333333 + 1.5625 Combine like terms: 0.3333333333 + 1.5625 = 1.8958333333 1.5625 + 2.5w + w2 = 1.8958333333 Factor a perfect square on the left side: (w + 1.25)(w + 1.25) = 1.8958333333 Calculate the square root of the right side: 1.376892637 Break this problem into two subproblems by setting (w + 1.25) equal to 1.376892637 and -1.376892637.Subproblem 1
w + 1.25 = 1.376892637 Simplifying w + 1.25 = 1.376892637 Reorder the terms: 1.25 + w = 1.376892637 Solving 1.25 + w = 1.376892637 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = 1.376892637 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = 1.376892637 + -1.25 w = 1.376892637 + -1.25 Combine like terms: 1.376892637 + -1.25 = 0.126892637 w = 0.126892637 Simplifying w = 0.126892637Subproblem 2
w + 1.25 = -1.376892637 Simplifying w + 1.25 = -1.376892637 Reorder the terms: 1.25 + w = -1.376892637 Solving 1.25 + w = -1.376892637 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + w = -1.376892637 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + w = -1.376892637 + -1.25 w = -1.376892637 + -1.25 Combine like terms: -1.376892637 + -1.25 = -2.626892637 w = -2.626892637 Simplifying w = -2.626892637Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.126892637, -2.626892637}Solution
w = {0.126892637, -2.626892637}
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