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Simplifying 2w2 + 2w + 8 = 16 Reorder the terms: 8 + 2w + 2w2 = 16 Solving 8 + 2w + 2w2 = 16 Solving for variable 'w'. Reorder the terms: 8 + -16 + 2w + 2w2 = 16 + -16 Combine like terms: 8 + -16 = -8 -8 + 2w + 2w2 = 16 + -16 Combine like terms: 16 + -16 = 0 -8 + 2w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + w + w2)' equal to zero and attempt to solve: Simplifying -4 + w + w2 = 0 Solving -4 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w + w2 = 0 + 4 w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 w + w2 = 4 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 4 + 0.25 Reorder the terms: 0.25 + w + w2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + w + w2 = 4.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (w + 0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
w + 0.5 = 2.061552813 Simplifying w + 0.5 = 2.061552813 Reorder the terms: 0.5 + w = 2.061552813 Solving 0.5 + w = 2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 2.061552813 + -0.5 w = 2.061552813 + -0.5 Combine like terms: 2.061552813 + -0.5 = 1.561552813 w = 1.561552813 Simplifying w = 1.561552813Subproblem 2
w + 0.5 = -2.061552813 Simplifying w + 0.5 = -2.061552813 Reorder the terms: 0.5 + w = -2.061552813 Solving 0.5 + w = -2.061552813 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -2.061552813 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -2.061552813 + -0.5 w = -2.061552813 + -0.5 Combine like terms: -2.061552813 + -0.5 = -2.561552813 w = -2.561552813 Simplifying w = -2.561552813Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.561552813, -2.561552813}Solution
w = {1.561552813, -2.561552813}
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