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Simplifying 3w2 + 12w + 3 = 0 Reorder the terms: 3 + 12w + 3w2 = 0 Solving 3 + 12w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 4w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 4w + w2)' equal to zero and attempt to solve: Simplifying 1 + 4w + w2 = 0 Solving 1 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4w + -1 + w2 = 0 + -1 Reorder the terms: 1 + -1 + 4w + w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4w + w2 = 0 + -1 4w + w2 = 0 + -1 Combine like terms: 0 + -1 = -1 4w + w2 = -1 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = -1 + 4 Reorder the terms: 4 + 4w + w2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4w + w2 = 3 Factor a perfect square on the left side: (w + 2)(w + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (w + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
w + 2 = 1.732050808 Simplifying w + 2 = 1.732050808 Reorder the terms: 2 + w = 1.732050808 Solving 2 + w = 1.732050808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + w = 1.732050808 + -2 w = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 w = -0.267949192 Simplifying w = -0.267949192Subproblem 2
w + 2 = -1.732050808 Simplifying w + 2 = -1.732050808 Reorder the terms: 2 + w = -1.732050808 Solving 2 + w = -1.732050808 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + w = -1.732050808 + -2 w = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 w = -3.732050808 Simplifying w = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. w = {-0.267949192, -3.732050808}Solution
w = {-0.267949192, -3.732050808}
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