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Simplifying (5w2) + 17w = 6 Reorder the terms: 17w + (5w2) = 6 Solving 17w + (5w2) = 6 Solving for variable 'w'. Reorder the terms: -6 + 17w + (5w2) = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 17w + (5w2) = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 3.4w + w2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 3.4w + 1.2 + w2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 3.4w + w2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 3.4w + w2 = 0 + 1.2 3.4w + w2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 3.4w + w2 = 1.2 The w term is 3.4w. Take half its coefficient (1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. 3.4w + 2.89 + w2 = 1.2 + 2.89 Reorder the terms: 2.89 + 3.4w + w2 = 1.2 + 2.89 Combine like terms: 1.2 + 2.89 = 4.09 2.89 + 3.4w + w2 = 4.09 Factor a perfect square on the left side: ((w) + 1.7)((w) + 1.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting ((w) + 1.7) equal to 2.022374842 and -2.022374842.Subproblem 1
(w) + 1.7 = 2.022374842 Simplifying (w) + 1.7 = 2.022374842 w + 1.7 = 2.022374842 Reorder the terms: 1.7 + w = 2.022374842 Solving 1.7 + w = 2.022374842 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + w = 2.022374842 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + w = 2.022374842 + -1.7 w = 2.022374842 + -1.7 Combine like terms: 2.022374842 + -1.7 = 0.322374842 w = 0.322374842 Simplifying w = 0.322374842Subproblem 2
(w) + 1.7 = -2.022374842 Simplifying (w) + 1.7 = -2.022374842 w + 1.7 = -2.022374842 Reorder the terms: 1.7 + w = -2.022374842 Solving 1.7 + w = -2.022374842 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + w = -2.022374842 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + w = -2.022374842 + -1.7 w = -2.022374842 + -1.7 Combine like terms: -2.022374842 + -1.7 = -3.722374842 w = -3.722374842 Simplifying w = -3.722374842Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.322374842, -3.722374842}
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