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Simplifying 5w2 + -19w + -80 = 0 Reorder the terms: -80 + -19w + 5w2 = 0 Solving -80 + -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'. -16 + -3.8w + w2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -3.8w + 16 + w2 = 0 + 16 Reorder the terms: -16 + 16 + -3.8w + w2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -3.8w + w2 = 0 + 16 -3.8w + w2 = 0 + 16 Combine like terms: 0 + 16 = 16 -3.8w + w2 = 16 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 = 16 + 3.61 Reorder the terms: 3.61 + -3.8w + w2 = 16 + 3.61 Combine like terms: 16 + 3.61 = 19.61 3.61 + -3.8w + w2 = 19.61 Factor a perfect square on the left side: (w + -1.9)(w + -1.9) = 19.61 Calculate the square root of the right side: 4.428317965 Break this problem into two subproblems by setting (w + -1.9) equal to 4.428317965 and -4.428317965.Subproblem 1
w + -1.9 = 4.428317965 Simplifying w + -1.9 = 4.428317965 Reorder the terms: -1.9 + w = 4.428317965 Solving -1.9 + w = 4.428317965 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 = 4.428317965 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = 4.428317965 + 1.9 w = 4.428317965 + 1.9 Combine like terms: 4.428317965 + 1.9 = 6.328317965 w = 6.328317965 Simplifying w = 6.328317965Subproblem 2
w + -1.9 = -4.428317965 Simplifying w + -1.9 = -4.428317965 Reorder the terms: -1.9 + w = -4.428317965 Solving -1.9 + w = -4.428317965 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 = -4.428317965 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = -4.428317965 + 1.9 w = -4.428317965 + 1.9 Combine like terms: -4.428317965 + 1.9 = -2.528317965 w = -2.528317965 Simplifying w = -2.528317965Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.328317965, -2.528317965}
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