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Simplifying w2 + 7w + -100 = 0 Reorder the terms: -100 + 7w + w2 = 0 Solving -100 + 7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 7w + 100 + w2 = 0 + 100 Reorder the terms: -100 + 100 + 7w + w2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 7w + w2 = 0 + 100 7w + w2 = 0 + 100 Combine like terms: 0 + 100 = 100 7w + w2 = 100 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 = 100 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 100 + 12.25 Combine like terms: 100 + 12.25 = 112.25 12.25 + 7w + w2 = 112.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (w + 3.5) equal to 10.59481005 and -10.59481005.Subproblem 1
w + 3.5 = 10.59481005 Simplifying w + 3.5 = 10.59481005 Reorder the terms: 3.5 + w = 10.59481005 Solving 3.5 + w = 10.59481005 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 = 10.59481005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 10.59481005 + -3.5 w = 10.59481005 + -3.5 Combine like terms: 10.59481005 + -3.5 = 7.09481005 w = 7.09481005 Simplifying w = 7.09481005Subproblem 2
w + 3.5 = -10.59481005 Simplifying w + 3.5 = -10.59481005 Reorder the terms: 3.5 + w = -10.59481005 Solving 3.5 + w = -10.59481005 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 = -10.59481005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -10.59481005 + -3.5 w = -10.59481005 + -3.5 Combine like terms: -10.59481005 + -3.5 = -14.09481005 w = -14.09481005 Simplifying w = -14.09481005Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.09481005, -14.09481005}
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