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Simplifying (w + -6)(w + 5) + -2 = -4 Reorder the terms: (-6 + w)(w + 5) + -2 = -4 Reorder the terms: (-6 + w)(5 + w) + -2 = -4 Multiply (-6 + w) * (5 + w) (-6(5 + w) + w(5 + w)) + -2 = -4 ((5 * -6 + w * -6) + w(5 + w)) + -2 = -4 ((-30 + -6w) + w(5 + w)) + -2 = -4 (-30 + -6w + (5 * w + w * w)) + -2 = -4 (-30 + -6w + (5w + w2)) + -2 = -4 Combine like terms: -6w + 5w = -1w (-30 + -1w + w2) + -2 = -4 Reorder the terms: -30 + -2 + -1w + w2 = -4 Combine like terms: -30 + -2 = -32 -32 + -1w + w2 = -4 Solving -32 + -1w + w2 = -4 Solving for variable 'w'. Reorder the terms: -32 + 4 + -1w + w2 = -4 + 4 Combine like terms: -32 + 4 = -28 -28 + -1w + w2 = -4 + 4 Combine like terms: -4 + 4 = 0 -28 + -1w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -1w + 28 + w2 = 0 + 28 Reorder the terms: -28 + 28 + -1w + w2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1w + w2 = 0 + 28 -1w + w2 = 0 + 28 Combine like terms: 0 + 28 = 28 -1w + w2 = 28 The w term is -1w. 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. -1w + 0.25 + w2 = 28 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + -1w + w2 = 28.25 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (w + -0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
w + -0.5 = 5.315072906 Simplifying w + -0.5 = 5.315072906 Reorder the terms: -0.5 + w = 5.315072906 Solving -0.5 + w = 5.315072906 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 = 5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 5.315072906 + 0.5 w = 5.315072906 + 0.5 Combine like terms: 5.315072906 + 0.5 = 5.815072906 w = 5.815072906 Simplifying w = 5.815072906Subproblem 2
w + -0.5 = -5.315072906 Simplifying w + -0.5 = -5.315072906 Reorder the terms: -0.5 + w = -5.315072906 Solving -0.5 + w = -5.315072906 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 = -5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -5.315072906 + 0.5 w = -5.315072906 + 0.5 Combine like terms: -5.315072906 + 0.5 = -4.815072906 w = -4.815072906 Simplifying w = -4.815072906Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.815072906, -4.815072906}
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