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Simplifying w2 + 7w + -14 = 0 Reorder the terms: -14 + 7w + w2 = 0 Solving -14 + 7w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 7w + 14 + w2 = 0 + 14 Reorder the terms: -14 + 14 + 7w + w2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 7w + w2 = 0 + 14 7w + w2 = 0 + 14 Combine like terms: 0 + 14 = 14 7w + w2 = 14 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 = 14 + 12.25 Reorder the terms: 12.25 + 7w + w2 = 14 + 12.25 Combine like terms: 14 + 12.25 = 26.25 12.25 + 7w + w2 = 26.25 Factor a perfect square on the left side: (w + 3.5)(w + 3.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (w + 3.5) equal to 5.123475383 and -5.123475383.Subproblem 1
w + 3.5 = 5.123475383 Simplifying w + 3.5 = 5.123475383 Reorder the terms: 3.5 + w = 5.123475383 Solving 3.5 + w = 5.123475383 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 = 5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = 5.123475383 + -3.5 w = 5.123475383 + -3.5 Combine like terms: 5.123475383 + -3.5 = 1.623475383 w = 1.623475383 Simplifying w = 1.623475383Subproblem 2
w + 3.5 = -5.123475383 Simplifying w + 3.5 = -5.123475383 Reorder the terms: 3.5 + w = -5.123475383 Solving 3.5 + w = -5.123475383 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 = -5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + w = -5.123475383 + -3.5 w = -5.123475383 + -3.5 Combine like terms: -5.123475383 + -3.5 = -8.623475383 w = -8.623475383 Simplifying w = -8.623475383Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.623475383, -8.623475383}
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