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Simplifying 5w2 + 19w + -1 = 0 Reorder the terms: -1 + 19w + 5w2 = 0 Solving -1 + 19w + 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'. -0.2 + 3.8w + w2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 3.8w + 0.2 + w2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 3.8w + w2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 3.8w + w2 = 0 + 0.2 3.8w + w2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 3.8w + w2 = 0.2 The w term is 3.8w. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8w + 3.61 + w2 = 0.2 + 3.61 Reorder the terms: 3.61 + 3.8w + w2 = 0.2 + 3.61 Combine like terms: 0.2 + 3.61 = 3.81 3.61 + 3.8w + w2 = 3.81 Factor a perfect square on the left side: (w + 1.9)(w + 1.9) = 3.81 Calculate the square root of the right side: 1.95192213 Break this problem into two subproblems by setting (w + 1.9) equal to 1.95192213 and -1.95192213.Subproblem 1
w + 1.9 = 1.95192213 Simplifying w + 1.9 = 1.95192213 Reorder the terms: 1.9 + w = 1.95192213 Solving 1.9 + w = 1.95192213 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + w = 1.95192213 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + w = 1.95192213 + -1.9 w = 1.95192213 + -1.9 Combine like terms: 1.95192213 + -1.9 = 0.05192213 w = 0.05192213 Simplifying w = 0.05192213Subproblem 2
w + 1.9 = -1.95192213 Simplifying w + 1.9 = -1.95192213 Reorder the terms: 1.9 + w = -1.95192213 Solving 1.9 + w = -1.95192213 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + w = -1.95192213 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + w = -1.95192213 + -1.9 w = -1.95192213 + -1.9 Combine like terms: -1.95192213 + -1.9 = -3.85192213 w = -3.85192213 Simplifying w = -3.85192213Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.05192213, -3.85192213}
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