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Simplifying 5 = 6w + 5w(w + -5) Reorder the terms: 5 = 6w + 5w(-5 + w) 5 = 6w + (-5 * 5w + w * 5w) 5 = 6w + (-25w + 5w2) Combine like terms: 6w + -25w = -19w 5 = -19w + 5w2 Solving 5 = -19w + 5w2 Solving for variable 'w'. Reorder the terms: 5 + 19w + -5w2 = -19w + 19w + 5w2 + -5w2 Combine like terms: -19w + 19w = 0 5 + 19w + -5w2 = 0 + 5w2 + -5w2 5 + 19w + -5w2 = 5w2 + -5w2 Combine like terms: 5w2 + -5w2 = 0 5 + 19w + -5w2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + -3.8w + w2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.8w + 1 + w2 = 0 + 1 Reorder the terms: -1 + 1 + -3.8w + w2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.8w + w2 = 0 + 1 -3.8w + w2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.8w + w2 = 1 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 = 1 + 3.61 Reorder the terms: 3.61 + -3.8w + w2 = 1 + 3.61 Combine like terms: 1 + 3.61 = 4.61 3.61 + -3.8w + w2 = 4.61 Factor a perfect square on the left side: (w + -1.9)(w + -1.9) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (w + -1.9) equal to 2.147091055 and -2.147091055.Subproblem 1
w + -1.9 = 2.147091055 Simplifying w + -1.9 = 2.147091055 Reorder the terms: -1.9 + w = 2.147091055 Solving -1.9 + w = 2.147091055 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 = 2.147091055 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = 2.147091055 + 1.9 w = 2.147091055 + 1.9 Combine like terms: 2.147091055 + 1.9 = 4.047091055 w = 4.047091055 Simplifying w = 4.047091055Subproblem 2
w + -1.9 = -2.147091055 Simplifying w + -1.9 = -2.147091055 Reorder the terms: -1.9 + w = -2.147091055 Solving -1.9 + w = -2.147091055 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 = -2.147091055 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + w = -2.147091055 + 1.9 w = -2.147091055 + 1.9 Combine like terms: -2.147091055 + 1.9 = -0.247091055 w = -0.247091055 Simplifying w = -0.247091055Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.047091055, -0.247091055}
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