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Simplifying w2 + 3w + -15 = 0 Reorder the terms: -15 + 3w + w2 = 0 Solving -15 + 3w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 3w + 15 + w2 = 0 + 15 Reorder the terms: -15 + 15 + 3w + w2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 3w + w2 = 0 + 15 3w + w2 = 0 + 15 Combine like terms: 0 + 15 = 15 3w + w2 = 15 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 = 15 + 2.25 Reorder the terms: 2.25 + 3w + w2 = 15 + 2.25 Combine like terms: 15 + 2.25 = 17.25 2.25 + 3w + w2 = 17.25 Factor a perfect square on the left side: (w + 1.5)(w + 1.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (w + 1.5) equal to 4.153311931 and -4.153311931.Subproblem 1
w + 1.5 = 4.153311931 Simplifying w + 1.5 = 4.153311931 Reorder the terms: 1.5 + w = 4.153311931 Solving 1.5 + w = 4.153311931 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 = 4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 4.153311931 + -1.5 w = 4.153311931 + -1.5 Combine like terms: 4.153311931 + -1.5 = 2.653311931 w = 2.653311931 Simplifying w = 2.653311931Subproblem 2
w + 1.5 = -4.153311931 Simplifying w + 1.5 = -4.153311931 Reorder the terms: 1.5 + w = -4.153311931 Solving 1.5 + w = -4.153311931 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 = -4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -4.153311931 + -1.5 w = -4.153311931 + -1.5 Combine like terms: -4.153311931 + -1.5 = -5.653311931 w = -5.653311931 Simplifying w = -5.653311931Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.653311931, -5.653311931}
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