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Simplifying w2 + 7w + -156 = 0 Reorder the terms: -156 + 7w + w2 = 0 Solving -156 + 7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + 7w + 156 + w2 = 0 + 156 Reorder the terms: -156 + 156 + 7w + w2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 7w + w2 = 0 + 156 7w + w2 = 0 + 156 Combine like terms: 0 + 156 = 156 7w + w2 = 156 The w term is 7w. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7w + 12.25 + w2 = 156 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 156 + 12.25 Combine like terms: 156 + 12.25 = 168.25 12.25 + 7w + w2 = 168.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 168.25 Calculate the square root of the right side: 12.971121771 Break this problem into two subproblems by setting (w + 3.5) equal to 12.971121771 and -12.971121771.Subproblem 1
w + 3.5 = 12.971121771 Simplifying w + 3.5 = 12.971121771 Reorder the terms: 3.5 + w = 12.971121771 Solving 3.5 + w = 12.971121771 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = 12.971121771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 12.971121771 + -3.5 w = 12.971121771 + -3.5 Combine like terms: 12.971121771 + -3.5 = 9.471121771 w = 9.471121771 Simplifying w = 9.471121771Subproblem 2
w + 3.5 = -12.971121771 Simplifying w + 3.5 = -12.971121771 Reorder the terms: 3.5 + w = -12.971121771 Solving 3.5 + w = -12.971121771 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + w = -12.971121771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -12.971121771 + -3.5 w = -12.971121771 + -3.5 Combine like terms: -12.971121771 + -3.5 = -16.471121771 w = -16.471121771 Simplifying w = -16.471121771Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.471121771, -16.471121771}
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