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Simplifying 5w2 = 31w + -28 Reorder the terms: 5w2 = -28 + 31w Solving 5w2 = -28 + 31w Solving for variable 'w'. Reorder the terms: 28 + -31w + 5w2 = -28 + 31w + 28 + -31w Reorder the terms: 28 + -31w + 5w2 = -28 + 28 + 31w + -31w Combine like terms: -28 + 28 = 0 28 + -31w + 5w2 = 0 + 31w + -31w 28 + -31w + 5w2 = 31w + -31w Combine like terms: 31w + -31w = 0 28 + -31w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.6 + -6.2w + w2 = 0 Move the constant term to the right: Add '-5.6' to each side of the equation. 5.6 + -6.2w + -5.6 + w2 = 0 + -5.6 Reorder the terms: 5.6 + -5.6 + -6.2w + w2 = 0 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + -6.2w + w2 = 0 + -5.6 -6.2w + w2 = 0 + -5.6 Combine like terms: 0 + -5.6 = -5.6 -6.2w + w2 = -5.6 The w term is -6.2w. Take half its coefficient (-3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. -6.2w + 9.61 + w2 = -5.6 + 9.61 Reorder the terms: 9.61 + -6.2w + w2 = -5.6 + 9.61 Combine like terms: -5.6 + 9.61 = 4.01 9.61 + -6.2w + w2 = 4.01 Factor a perfect square on the left side: (w + -3.1)(w + -3.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (w + -3.1) equal to 2.002498439 and -2.002498439.Subproblem 1
w + -3.1 = 2.002498439 Simplifying w + -3.1 = 2.002498439 Reorder the terms: -3.1 + w = 2.002498439 Solving -3.1 + w = 2.002498439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + w = 2.002498439 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + w = 2.002498439 + 3.1 w = 2.002498439 + 3.1 Combine like terms: 2.002498439 + 3.1 = 5.102498439 w = 5.102498439 Simplifying w = 5.102498439Subproblem 2
w + -3.1 = -2.002498439 Simplifying w + -3.1 = -2.002498439 Reorder the terms: -3.1 + w = -2.002498439 Solving -3.1 + w = -2.002498439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.1' to each side of the equation. -3.1 + 3.1 + w = -2.002498439 + 3.1 Combine like terms: -3.1 + 3.1 = 0.0 0.0 + w = -2.002498439 + 3.1 w = -2.002498439 + 3.1 Combine like terms: -2.002498439 + 3.1 = 1.097501561 w = 1.097501561 Simplifying w = 1.097501561Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.102498439, 1.097501561}
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