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Simplifying 5w2 + -19w + -20 = 0 Reorder the terms: -20 + -19w + 5w2 = 0 Solving -20 + -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'. -4 + -3.8w + w2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.8w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -3.8w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.8w + w2 = 0 + 4 -3.8w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.8w + w2 = 4 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 = 4 + 3.61 Reorder the terms: 3.61 + -3.8w + w2 = 4 + 3.61 Combine like terms: 4 + 3.61 = 7.61 3.61 + -3.8w + w2 = 7.61 Factor a perfect square on the left side: (w + -1.9)(w + -1.9) = 7.61 Calculate the square root of the right side: 2.758622845 Break this problem into two subproblems by setting (w + -1.9) equal to 2.758622845 and -2.758622845.Subproblem 1
w + -1.9 = 2.758622845 Simplifying w + -1.9 = 2.758622845 Reorder the terms: -1.9 + w = 2.758622845 Solving -1.9 + w = 2.758622845 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 = 2.758622845 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = 2.758622845 + 1.9 w = 2.758622845 + 1.9 Combine like terms: 2.758622845 + 1.9 = 4.658622845 w = 4.658622845 Simplifying w = 4.658622845Subproblem 2
w + -1.9 = -2.758622845 Simplifying w + -1.9 = -2.758622845 Reorder the terms: -1.9 + w = -2.758622845 Solving -1.9 + w = -2.758622845 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 = -2.758622845 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = -2.758622845 + 1.9 w = -2.758622845 + 1.9 Combine like terms: -2.758622845 + 1.9 = -0.858622845 w = -0.858622845 Simplifying w = -0.858622845Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.658622845, -0.858622845}
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