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Simplifying 4w2 + 32w = 220 Reorder the terms: 32w + 4w2 = 220 Solving 32w + 4w2 = 220 Solving for variable 'w'. Reorder the terms: -220 + 32w + 4w2 = 220 + -220 Combine like terms: 220 + -220 = 0 -220 + 32w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-55 + 8w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-55 + 8w + w2)' equal to zero and attempt to solve: Simplifying -55 + 8w + w2 = 0 Solving -55 + 8w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 8w + 55 + w2 = 0 + 55 Reorder the terms: -55 + 55 + 8w + w2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 8w + w2 = 0 + 55 8w + w2 = 0 + 55 Combine like terms: 0 + 55 = 55 8w + w2 = 55 The w term is 8w. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8w + 16 + w2 = 55 + 16 Reorder the terms: 16 + 8w + w2 = 55 + 16 Combine like terms: 55 + 16 = 71 16 + 8w + w2 = 71 Factor a perfect square on the left side: (w + 4)(w + 4) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (w + 4) equal to 8.426149773 and -8.426149773.Subproblem 1
w + 4 = 8.426149773 Simplifying w + 4 = 8.426149773 Reorder the terms: 4 + w = 8.426149773 Solving 4 + w = 8.426149773 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = 8.426149773 + -4 Combine like terms: 4 + -4 = 0 0 + w = 8.426149773 + -4 w = 8.426149773 + -4 Combine like terms: 8.426149773 + -4 = 4.426149773 w = 4.426149773 Simplifying w = 4.426149773Subproblem 2
w + 4 = -8.426149773 Simplifying w + 4 = -8.426149773 Reorder the terms: 4 + w = -8.426149773 Solving 4 + w = -8.426149773 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + w = -8.426149773 + -4 Combine like terms: 4 + -4 = 0 0 + w = -8.426149773 + -4 w = -8.426149773 + -4 Combine like terms: -8.426149773 + -4 = -12.426149773 w = -12.426149773 Simplifying w = -12.426149773Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.426149773, -12.426149773}Solution
w = {4.426149773, -12.426149773}
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