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Simplifying w + (w2 + 11) = 63 Reorder the terms: w + (11 + w2) = 63 Remove parenthesis around (11 + w2) w + 11 + w2 = 63 Reorder the terms: 11 + w + w2 = 63 Solving 11 + w + w2 = 63 Solving for variable 'w'. Reorder the terms: 11 + -63 + w + w2 = 63 + -63 Combine like terms: 11 + -63 = -52 -52 + w + w2 = 63 + -63 Combine like terms: 63 + -63 = 0 -52 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + w + 52 + w2 = 0 + 52 Reorder the terms: -52 + 52 + w + w2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + w + w2 = 0 + 52 w + w2 = 0 + 52 Combine like terms: 0 + 52 = 52 w + w2 = 52 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 52 + 0.25 Reorder the terms: 0.25 + w + w2 = 52 + 0.25 Combine like terms: 52 + 0.25 = 52.25 0.25 + w + w2 = 52.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (w + 0.5) equal to 7.228416147 and -7.228416147.Subproblem 1
w + 0.5 = 7.228416147 Simplifying w + 0.5 = 7.228416147 Reorder the terms: 0.5 + w = 7.228416147 Solving 0.5 + w = 7.228416147 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 7.228416147 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 7.228416147 + -0.5 w = 7.228416147 + -0.5 Combine like terms: 7.228416147 + -0.5 = 6.728416147 w = 6.728416147 Simplifying w = 6.728416147Subproblem 2
w + 0.5 = -7.228416147 Simplifying w + 0.5 = -7.228416147 Reorder the terms: 0.5 + w = -7.228416147 Solving 0.5 + w = -7.228416147 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -7.228416147 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -7.228416147 + -0.5 w = -7.228416147 + -0.5 Combine like terms: -7.228416147 + -0.5 = -7.728416147 w = -7.728416147 Simplifying w = -7.728416147Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.728416147, -7.728416147}
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