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Simplifying 400 = 2w2 + 4w Reorder the terms: 400 = 4w + 2w2 Solving 400 = 4w + 2w2 Solving for variable 'w'. Reorder the terms: 400 + -4w + -2w2 = 4w + -4w + 2w2 + -2w2 Combine like terms: 4w + -4w = 0 400 + -4w + -2w2 = 0 + 2w2 + -2w2 400 + -4w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 400 + -4w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + -2w + -1w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + -2w + -1w2)' equal to zero and attempt to solve: Simplifying 200 + -2w + -1w2 = 0 Solving 200 + -2w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + 2w + w2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 2w + 200 + w2 = 0 + 200 Reorder the terms: -200 + 200 + 2w + w2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 2w + w2 = 0 + 200 2w + w2 = 0 + 200 Combine like terms: 0 + 200 = 200 2w + w2 = 200 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 200 + 1 Reorder the terms: 1 + 2w + w2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + 2w + w2 = 201 Factor a perfect square on the left side: (w + 1)(w + 1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (w + 1) equal to 14.177446879 and -14.177446879.Subproblem 1
w + 1 = 14.177446879 Simplifying w + 1 = 14.177446879 Reorder the terms: 1 + w = 14.177446879 Solving 1 + w = 14.177446879 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + w = 14.177446879 + -1 w = 14.177446879 + -1 Combine like terms: 14.177446879 + -1 = 13.177446879 w = 13.177446879 Simplifying w = 13.177446879Subproblem 2
w + 1 = -14.177446879 Simplifying w + 1 = -14.177446879 Reorder the terms: 1 + w = -14.177446879 Solving 1 + w = -14.177446879 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + w = -14.177446879 + -1 w = -14.177446879 + -1 Combine like terms: -14.177446879 + -1 = -15.177446879 w = -15.177446879 Simplifying w = -15.177446879Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.177446879, -15.177446879}Solution
w = {13.177446879, -15.177446879}
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