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Simplifying 5w2 + 20w + -24 = 0 Reorder the terms: -24 + 20w + 5w2 = 0 Solving -24 + 20w + 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'. -4.8 + 4w + w2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 4w + 4.8 + w2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 4w + w2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4w + w2 = 0 + 4.8 4w + w2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 4w + w2 = 4.8 The w term is 4w. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4w + 4 + w2 = 4.8 + 4 Reorder the terms: 4 + 4w + w2 = 4.8 + 4 Combine like terms: 4.8 + 4 = 8.8 4 + 4w + w2 = 8.8 Factor a perfect square on the left side: (w + 2)(w + 2) = 8.8 Calculate the square root of the right side: 2.966479395 Break this problem into two subproblems by setting (w + 2) equal to 2.966479395 and -2.966479395.Subproblem 1
w + 2 = 2.966479395 Simplifying w + 2 = 2.966479395 Reorder the terms: 2 + w = 2.966479395 Solving 2 + w = 2.966479395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 2.966479395 + -2 Combine like terms: 2 + -2 = 0 0 + w = 2.966479395 + -2 w = 2.966479395 + -2 Combine like terms: 2.966479395 + -2 = 0.966479395 w = 0.966479395 Simplifying w = 0.966479395Subproblem 2
w + 2 = -2.966479395 Simplifying w + 2 = -2.966479395 Reorder the terms: 2 + w = -2.966479395 Solving 2 + w = -2.966479395 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -2.966479395 + -2 Combine like terms: 2 + -2 = 0 0 + w = -2.966479395 + -2 w = -2.966479395 + -2 Combine like terms: -2.966479395 + -2 = -4.966479395 w = -4.966479395 Simplifying w = -4.966479395Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.966479395, -4.966479395}
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