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Simplifying w2 + 4w + -133 = 0 Reorder the terms: -133 + 4w + w2 = 0 Solving -133 + 4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '133' to each side of the equation. -133 + 4w + 133 + w2 = 0 + 133 Reorder the terms: -133 + 133 + 4w + w2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + 4w + w2 = 0 + 133 4w + w2 = 0 + 133 Combine like terms: 0 + 133 = 133 4w + w2 = 133 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 = 133 + 4 Reorder the terms: 4 + 4w + w2 = 133 + 4 Combine like terms: 133 + 4 = 137 4 + 4w + w2 = 137 Factor a perfect square on the left side: (w + 2)(w + 2) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (w + 2) equal to 11.704699911 and -11.704699911.Subproblem 1
w + 2 = 11.704699911 Simplifying w + 2 = 11.704699911 Reorder the terms: 2 + w = 11.704699911 Solving 2 + w = 11.704699911 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 = 11.704699911 + -2 Combine like terms: 2 + -2 = 0 0 + w = 11.704699911 + -2 w = 11.704699911 + -2 Combine like terms: 11.704699911 + -2 = 9.704699911 w = 9.704699911 Simplifying w = 9.704699911Subproblem 2
w + 2 = -11.704699911 Simplifying w + 2 = -11.704699911 Reorder the terms: 2 + w = -11.704699911 Solving 2 + w = -11.704699911 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 = -11.704699911 + -2 Combine like terms: 2 + -2 = 0 0 + w = -11.704699911 + -2 w = -11.704699911 + -2 Combine like terms: -11.704699911 + -2 = -13.704699911 w = -13.704699911 Simplifying w = -13.704699911Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.704699911, -13.704699911}
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