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Simplifying w2 + 16w + -76 = 0 Reorder the terms: -76 + 16w + w2 = 0 Solving -76 + 16w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 16w + 76 + w2 = 0 + 76 Reorder the terms: -76 + 76 + 16w + w2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 16w + w2 = 0 + 76 16w + w2 = 0 + 76 Combine like terms: 0 + 76 = 76 16w + w2 = 76 The w term is 16w. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16w + 64 + w2 = 76 + 64 Reorder the terms: 64 + 16w + w2 = 76 + 64 Combine like terms: 76 + 64 = 140 64 + 16w + w2 = 140 Factor a perfect square on the left side: (w + 8)(w + 8) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (w + 8) equal to 11.832159566 and -11.832159566.Subproblem 1
w + 8 = 11.832159566 Simplifying w + 8 = 11.832159566 Reorder the terms: 8 + w = 11.832159566 Solving 8 + w = 11.832159566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + w = 11.832159566 + -8 w = 11.832159566 + -8 Combine like terms: 11.832159566 + -8 = 3.832159566 w = 3.832159566 Simplifying w = 3.832159566Subproblem 2
w + 8 = -11.832159566 Simplifying w + 8 = -11.832159566 Reorder the terms: 8 + w = -11.832159566 Solving 8 + w = -11.832159566 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = -11.832159566 + -8 Combine like terms: 8 + -8 = 0 0 + w = -11.832159566 + -8 w = -11.832159566 + -8 Combine like terms: -11.832159566 + -8 = -19.832159566 w = -19.832159566 Simplifying w = -19.832159566Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.832159566, -19.832159566}
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