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Simplifying 5w2 + -17w + -11.56 = 0 Reorder the terms: -11.56 + -17w + 5w2 = 0 Solving -11.56 + -17w + 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'. -2.312 + -3.4w + w2 = 0 Move the constant term to the right: Add '2.312' to each side of the equation. -2.312 + -3.4w + 2.312 + w2 = 0 + 2.312 Reorder the terms: -2.312 + 2.312 + -3.4w + w2 = 0 + 2.312 Combine like terms: -2.312 + 2.312 = 0.000 0.000 + -3.4w + w2 = 0 + 2.312 -3.4w + w2 = 0 + 2.312 Combine like terms: 0 + 2.312 = 2.312 -3.4w + w2 = 2.312 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 = 2.312 + 2.89 Reorder the terms: 2.89 + -3.4w + w2 = 2.312 + 2.89 Combine like terms: 2.312 + 2.89 = 5.202 2.89 + -3.4w + w2 = 5.202 Factor a perfect square on the left side: (w + -1.7)(w + -1.7) = 5.202 Calculate the square root of the right side: 2.280789337 Break this problem into two subproblems by setting (w + -1.7) equal to 2.280789337 and -2.280789337.Subproblem 1
w + -1.7 = 2.280789337 Simplifying w + -1.7 = 2.280789337 Reorder the terms: -1.7 + w = 2.280789337 Solving -1.7 + w = 2.280789337 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 = 2.280789337 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + w = 2.280789337 + 1.7 w = 2.280789337 + 1.7 Combine like terms: 2.280789337 + 1.7 = 3.980789337 w = 3.980789337 Simplifying w = 3.980789337Subproblem 2
w + -1.7 = -2.280789337 Simplifying w + -1.7 = -2.280789337 Reorder the terms: -1.7 + w = -2.280789337 Solving -1.7 + w = -2.280789337 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 = -2.280789337 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + w = -2.280789337 + 1.7 w = -2.280789337 + 1.7 Combine like terms: -2.280789337 + 1.7 = -0.580789337 w = -0.580789337 Simplifying w = -0.580789337Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.980789337, -0.580789337}
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