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Simplifying 2w2 + 6w + -16 = 0 Reorder the terms: -16 + 6w + 2w2 = 0 Solving -16 + 6w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 3w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 3w + w2)' equal to zero and attempt to solve: Simplifying -8 + 3w + w2 = 0 Solving -8 + 3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 3w + 8 + w2 = 0 + 8 Reorder the terms: -8 + 8 + 3w + w2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3w + w2 = 0 + 8 3w + w2 = 0 + 8 Combine like terms: 0 + 8 = 8 3w + w2 = 8 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 8 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + 3w + w2 = 10.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (w + 1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
w + 1.5 = 3.201562119 Simplifying w + 1.5 = 3.201562119 Reorder the terms: 1.5 + w = 3.201562119 Solving 1.5 + w = 3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 3.201562119 + -1.5 w = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 w = 1.701562119 Simplifying w = 1.701562119Subproblem 2
w + 1.5 = -3.201562119 Simplifying w + 1.5 = -3.201562119 Reorder the terms: 1.5 + w = -3.201562119 Solving 1.5 + w = -3.201562119 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -3.201562119 + -1.5 w = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 w = -4.701562119 Simplifying w = -4.701562119Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.701562119, -4.701562119}Solution
w = {1.701562119, -4.701562119}
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