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Simplifying 5w2 + -1w = 20 Reorder the terms: -1w + 5w2 = 20 Solving -1w + 5w2 = 20 Solving for variable 'w'. Reorder the terms: -20 + -1w + 5w2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -1w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -0.2w + w2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.2w + 4 + w2 = 0 + 4 Reorder the terms: -4 + 4 + -0.2w + w2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.2w + w2 = 0 + 4 -0.2w + w2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.2w + w2 = 4 The w term is -0.2w. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2w + 0.01 + w2 = 4 + 0.01 Reorder the terms: 0.01 + -0.2w + w2 = 4 + 0.01 Combine like terms: 4 + 0.01 = 4.01 0.01 + -0.2w + w2 = 4.01 Factor a perfect square on the left side: (w + -0.1)(w + -0.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (w + -0.1) equal to 2.002498439 and -2.002498439.Subproblem 1
w + -0.1 = 2.002498439 Simplifying w + -0.1 = 2.002498439 Reorder the terms: -0.1 + w = 2.002498439 Solving -0.1 + w = 2.002498439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + w = 2.002498439 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + w = 2.002498439 + 0.1 w = 2.002498439 + 0.1 Combine like terms: 2.002498439 + 0.1 = 2.102498439 w = 2.102498439 Simplifying w = 2.102498439Subproblem 2
w + -0.1 = -2.002498439 Simplifying w + -0.1 = -2.002498439 Reorder the terms: -0.1 + w = -2.002498439 Solving -0.1 + w = -2.002498439 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + w = -2.002498439 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + w = -2.002498439 + 0.1 w = -2.002498439 + 0.1 Combine like terms: -2.002498439 + 0.1 = -1.902498439 w = -1.902498439 Simplifying w = -1.902498439Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.102498439, -1.902498439}
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