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Simplifying 0.4w2 + 1.4w + -0.8 = 0 Reorder the terms: -0.8 + 1.4w + 0.4w2 = 0 Solving -0.8 + 1.4w + 0.4w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -2 + 3.5w + w2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.5w + 2 + w2 = 0 + 2 Reorder the terms: -2 + 2 + 3.5w + w2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.5w + w2 = 0 + 2 3.5w + w2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.5w + w2 = 2 The w term is 3.5w. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5w + 3.0625 + w2 = 2 + 3.0625 Reorder the terms: 3.0625 + 3.5w + w2 = 2 + 3.0625 Combine like terms: 2 + 3.0625 = 5.0625 3.0625 + 3.5w + w2 = 5.0625 Factor a perfect square on the left side: (w + 1.75)(w + 1.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (w + 1.75) equal to 2.25 and -2.25.Subproblem 1
w + 1.75 = 2.25 Simplifying w + 1.75 = 2.25 Reorder the terms: 1.75 + w = 2.25 Solving 1.75 + w = 2.25 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = 2.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = 2.25 + -1.75 w = 2.25 + -1.75 Combine like terms: 2.25 + -1.75 = 0.5 w = 0.5 Simplifying w = 0.5Subproblem 2
w + 1.75 = -2.25 Simplifying w + 1.75 = -2.25 Reorder the terms: 1.75 + w = -2.25 Solving 1.75 + w = -2.25 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + w = -2.25 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + w = -2.25 + -1.75 w = -2.25 + -1.75 Combine like terms: -2.25 + -1.75 = -4 w = -4 Simplifying w = -4Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.5, -4}
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