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Simplifying 25w2 + -10w + -31 = 0 Reorder the terms: -31 + -10w + 25w2 = 0 Solving -31 + -10w + 25w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.24 + -0.4w + w2 = 0 Move the constant term to the right: Add '1.24' to each side of the equation. -1.24 + -0.4w + 1.24 + w2 = 0 + 1.24 Reorder the terms: -1.24 + 1.24 + -0.4w + w2 = 0 + 1.24 Combine like terms: -1.24 + 1.24 = 0.00 0.00 + -0.4w + w2 = 0 + 1.24 -0.4w + w2 = 0 + 1.24 Combine like terms: 0 + 1.24 = 1.24 -0.4w + w2 = 1.24 The w term is -0.4w. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4w + 0.04 + w2 = 1.24 + 0.04 Reorder the terms: 0.04 + -0.4w + w2 = 1.24 + 0.04 Combine like terms: 1.24 + 0.04 = 1.28 0.04 + -0.4w + w2 = 1.28 Factor a perfect square on the left side: (w + -0.2)(w + -0.2) = 1.28 Calculate the square root of the right side: 1.13137085 Break this problem into two subproblems by setting (w + -0.2) equal to 1.13137085 and -1.13137085.Subproblem 1
w + -0.2 = 1.13137085 Simplifying w + -0.2 = 1.13137085 Reorder the terms: -0.2 + w = 1.13137085 Solving -0.2 + w = 1.13137085 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + w = 1.13137085 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + w = 1.13137085 + 0.2 w = 1.13137085 + 0.2 Combine like terms: 1.13137085 + 0.2 = 1.33137085 w = 1.33137085 Simplifying w = 1.33137085Subproblem 2
w + -0.2 = -1.13137085 Simplifying w + -0.2 = -1.13137085 Reorder the terms: -0.2 + w = -1.13137085 Solving -0.2 + w = -1.13137085 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + w = -1.13137085 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + w = -1.13137085 + 0.2 w = -1.13137085 + 0.2 Combine like terms: -1.13137085 + 0.2 = -0.93137085 w = -0.93137085 Simplifying w = -0.93137085Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.33137085, -0.93137085}
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