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Simplifying w2 + -4w + -594 = 0 Reorder the terms: -594 + -4w + w2 = 0 Solving -594 + -4w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '594' to each side of the equation. -594 + -4w + 594 + w2 = 0 + 594 Reorder the terms: -594 + 594 + -4w + w2 = 0 + 594 Combine like terms: -594 + 594 = 0 0 + -4w + w2 = 0 + 594 -4w + w2 = 0 + 594 Combine like terms: 0 + 594 = 594 -4w + w2 = 594 The w term is -4w. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4w + 4 + w2 = 594 + 4 Reorder the terms: 4 + -4w + w2 = 594 + 4 Combine like terms: 594 + 4 = 598 4 + -4w + w2 = 598 Factor a perfect square on the left side: (w + -2)(w + -2) = 598 Calculate the square root of the right side: 24.454038521 Break this problem into two subproblems by setting (w + -2) equal to 24.454038521 and -24.454038521.Subproblem 1
w + -2 = 24.454038521 Simplifying w + -2 = 24.454038521 Reorder the terms: -2 + w = 24.454038521 Solving -2 + w = 24.454038521 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 24.454038521 + 2 Combine like terms: -2 + 2 = 0 0 + w = 24.454038521 + 2 w = 24.454038521 + 2 Combine like terms: 24.454038521 + 2 = 26.454038521 w = 26.454038521 Simplifying w = 26.454038521Subproblem 2
w + -2 = -24.454038521 Simplifying w + -2 = -24.454038521 Reorder the terms: -2 + w = -24.454038521 Solving -2 + w = -24.454038521 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -24.454038521 + 2 Combine like terms: -2 + 2 = 0 0 + w = -24.454038521 + 2 w = -24.454038521 + 2 Combine like terms: -24.454038521 + 2 = -22.454038521 w = -22.454038521 Simplifying w = -22.454038521Solution
The solution to the problem is based on the solutions from the subproblems. w = {26.454038521, -22.454038521}
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