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Simplifying w2 + 4w = 800 Reorder the terms: 4w + w2 = 800 Solving 4w + w2 = 800 Solving for variable 'w'. Reorder the terms: -800 + 4w + w2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 4w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 4w + 800 + w2 = 0 + 800 Reorder the terms: -800 + 800 + 4w + w2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 4w + w2 = 0 + 800 4w + w2 = 0 + 800 Combine like terms: 0 + 800 = 800 4w + w2 = 800 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 800 + 4 Reorder the terms: 4 + 4w + w2 = 800 + 4 Combine like terms: 800 + 4 = 804 4 + 4w + w2 = 804 Factor a perfect square on the left side: (w + 2)(w + 2) = 804 Calculate the square root of the right side: 28.354893758 Break this problem into two subproblems by setting (w + 2) equal to 28.354893758 and -28.354893758.Subproblem 1
w + 2 = 28.354893758 Simplifying w + 2 = 28.354893758 Reorder the terms: 2 + w = 28.354893758 Solving 2 + w = 28.354893758 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 28.354893758 + -2 Combine like terms: 2 + -2 = 0 0 + w = 28.354893758 + -2 w = 28.354893758 + -2 Combine like terms: 28.354893758 + -2 = 26.354893758 w = 26.354893758 Simplifying w = 26.354893758Subproblem 2
w + 2 = -28.354893758 Simplifying w + 2 = -28.354893758 Reorder the terms: 2 + w = -28.354893758 Solving 2 + w = -28.354893758 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -28.354893758 + -2 Combine like terms: 2 + -2 = 0 0 + w = -28.354893758 + -2 w = -28.354893758 + -2 Combine like terms: -28.354893758 + -2 = -30.354893758 w = -30.354893758 Simplifying w = -30.354893758Solution
The solution to the problem is based on the solutions from the subproblems. w = {26.354893758, -30.354893758}
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