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Simplifying 2w2 + -12w = -12 Reorder the terms: -12w + 2w2 = -12 Solving -12w + 2w2 = -12 Solving for variable 'w'. Reorder the terms: 12 + -12w + 2w2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + -12w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -6w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -6w + w2)' equal to zero and attempt to solve: Simplifying 6 + -6w + w2 = 0 Solving 6 + -6w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -6w + -6 + w2 = 0 + -6 Reorder the terms: 6 + -6 + -6w + w2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6w + w2 = 0 + -6 -6w + w2 = 0 + -6 Combine like terms: 0 + -6 = -6 -6w + w2 = -6 The w term is -6w. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6w + 9 + w2 = -6 + 9 Reorder the terms: 9 + -6w + w2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6w + w2 = 3 Factor a perfect square on the left side: (w + -3)(w + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (w + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
w + -3 = 1.732050808 Simplifying w + -3 = 1.732050808 Reorder the terms: -3 + w = 1.732050808 Solving -3 + w = 1.732050808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + w = 1.732050808 + 3 w = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 w = 4.732050808 Simplifying w = 4.732050808Subproblem 2
w + -3 = -1.732050808 Simplifying w + -3 = -1.732050808 Reorder the terms: -3 + w = -1.732050808 Solving -3 + w = -1.732050808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + w = -1.732050808 + 3 w = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 w = 1.267949192 Simplifying w = 1.267949192Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.732050808, 1.267949192}Solution
w = {4.732050808, 1.267949192}
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