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Simplifying w2 + w = 3 Reorder the terms: w + w2 = 3 Solving w + w2 = 3 Solving for variable 'w'. Reorder the terms: -3 + w + w2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w + w2 = 0 + 3 w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 w + w2 = 3 The w term is w. 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. w + 0.25 + w2 = 3 + 0.25 Reorder the terms: 0.25 + w + w2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + w + w2 = 3.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (w + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
w + 0.5 = 1.802775638 Simplifying w + 0.5 = 1.802775638 Reorder the terms: 0.5 + w = 1.802775638 Solving 0.5 + w = 1.802775638 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 = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 1.802775638 + -0.5 w = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 w = 1.302775638 Simplifying w = 1.302775638Subproblem 2
w + 0.5 = -1.802775638 Simplifying w + 0.5 = -1.802775638 Reorder the terms: 0.5 + w = -1.802775638 Solving 0.5 + w = -1.802775638 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 = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -1.802775638 + -0.5 w = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 w = -2.302775638 Simplifying w = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.302775638, -2.302775638}
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