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Simplifying 5w2 + -5w + -17 = 0 Reorder the terms: -17 + -5w + 5w2 = 0 Solving -17 + -5w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + -1w + w2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + -1w + 3.4 + w2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + -1w + w2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + -1w + w2 = 0 + 3.4 -1w + w2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 -1w + w2 = 3.4 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 = 3.4 + 0.25 Reorder the terms: 0.25 + -1w + w2 = 3.4 + 0.25 Combine like terms: 3.4 + 0.25 = 3.65 0.25 + -1w + w2 = 3.65 Factor a perfect square on the left side: (w + -0.5)(w + -0.5) = 3.65 Calculate the square root of the right side: 1.910497317 Break this problem into two subproblems by setting (w + -0.5) equal to 1.910497317 and -1.910497317.Subproblem 1
w + -0.5 = 1.910497317 Simplifying w + -0.5 = 1.910497317 Reorder the terms: -0.5 + w = 1.910497317 Solving -0.5 + w = 1.910497317 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 = 1.910497317 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 1.910497317 + 0.5 w = 1.910497317 + 0.5 Combine like terms: 1.910497317 + 0.5 = 2.410497317 w = 2.410497317 Simplifying w = 2.410497317Subproblem 2
w + -0.5 = -1.910497317 Simplifying w + -0.5 = -1.910497317 Reorder the terms: -0.5 + w = -1.910497317 Solving -0.5 + w = -1.910497317 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 = -1.910497317 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -1.910497317 + 0.5 w = -1.910497317 + 0.5 Combine like terms: -1.910497317 + 0.5 = -1.410497317 w = -1.410497317 Simplifying w = -1.410497317Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.410497317, -1.410497317}
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