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Simplifying 4w2 + 80w = 400 Reorder the terms: 80w + 4w2 = 400 Solving 80w + 4w2 = 400 Solving for variable 'w'. Reorder the terms: -400 + 80w + 4w2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 80w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-100 + 20w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-100 + 20w + w2)' equal to zero and attempt to solve: Simplifying -100 + 20w + w2 = 0 Solving -100 + 20w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 20w + 100 + w2 = 0 + 100 Reorder the terms: -100 + 100 + 20w + w2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 20w + w2 = 0 + 100 20w + w2 = 0 + 100 Combine like terms: 0 + 100 = 100 20w + w2 = 100 The w term is 20w. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20w + 100 + w2 = 100 + 100 Reorder the terms: 100 + 20w + w2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + 20w + w2 = 200 Factor a perfect square on the left side: (w + 10)(w + 10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (w + 10) equal to 14.142135624 and -14.142135624.Subproblem 1
w + 10 = 14.142135624 Simplifying w + 10 = 14.142135624 Reorder the terms: 10 + w = 14.142135624 Solving 10 + w = 14.142135624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + w = 14.142135624 + -10 w = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 w = 4.142135624 Simplifying w = 4.142135624Subproblem 2
w + 10 = -14.142135624 Simplifying w + 10 = -14.142135624 Reorder the terms: 10 + w = -14.142135624 Solving 10 + w = -14.142135624 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + w = -14.142135624 + -10 w = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 w = -24.142135624 Simplifying w = -24.142135624Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.142135624, -24.142135624}Solution
w = {4.142135624, -24.142135624}
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