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Simplifying w2 + 3w + -3 = 0 Reorder the terms: -3 + 3w + w2 = 0 Solving -3 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + 3w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3w + w2 = 0 + 3 3w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 3w + w2 = 3 The w term is 3w. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3w + 2.25 + w2 = 3 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3w + w2 = 5.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (w + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
w + 1.5 = 2.291287847 Simplifying w + 1.5 = 2.291287847 Reorder the terms: 1.5 + w = 2.291287847 Solving 1.5 + w = 2.291287847 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 2.291287847 + -1.5 w = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 w = 0.791287847 Simplifying w = 0.791287847Subproblem 2
w + 1.5 = -2.291287847 Simplifying w + 1.5 = -2.291287847 Reorder the terms: 1.5 + w = -2.291287847 Solving 1.5 + w = -2.291287847 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -2.291287847 + -1.5 w = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 w = -3.791287847 Simplifying w = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.791287847, -3.791287847}
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