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Simplifying 50w2 + -23w = 63 Reorder the terms: -23w + 50w2 = 63 Solving -23w + 50w2 = 63 Solving for variable 'w'. Reorder the terms: -63 + -23w + 50w2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -23w + 50w2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.26 + -0.46w + w2 = 0 Move the constant term to the right: Add '1.26' to each side of the equation. -1.26 + -0.46w + 1.26 + w2 = 0 + 1.26 Reorder the terms: -1.26 + 1.26 + -0.46w + w2 = 0 + 1.26 Combine like terms: -1.26 + 1.26 = 0.00 0.00 + -0.46w + w2 = 0 + 1.26 -0.46w + w2 = 0 + 1.26 Combine like terms: 0 + 1.26 = 1.26 -0.46w + w2 = 1.26 The w term is -0.46w. Take half its coefficient (-0.23). Square it (0.0529) and add it to both sides. Add '0.0529' to each side of the equation. -0.46w + 0.0529 + w2 = 1.26 + 0.0529 Reorder the terms: 0.0529 + -0.46w + w2 = 1.26 + 0.0529 Combine like terms: 1.26 + 0.0529 = 1.3129 0.0529 + -0.46w + w2 = 1.3129 Factor a perfect square on the left side: (w + -0.23)(w + -0.23) = 1.3129 Calculate the square root of the right side: 1.145818485 Break this problem into two subproblems by setting (w + -0.23) equal to 1.145818485 and -1.145818485.Subproblem 1
w + -0.23 = 1.145818485 Simplifying w + -0.23 = 1.145818485 Reorder the terms: -0.23 + w = 1.145818485 Solving -0.23 + w = 1.145818485 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.23' to each side of the equation. -0.23 + 0.23 + w = 1.145818485 + 0.23 Combine like terms: -0.23 + 0.23 = 0.00 0.00 + w = 1.145818485 + 0.23 w = 1.145818485 + 0.23 Combine like terms: 1.145818485 + 0.23 = 1.375818485 w = 1.375818485 Simplifying w = 1.375818485Subproblem 2
w + -0.23 = -1.145818485 Simplifying w + -0.23 = -1.145818485 Reorder the terms: -0.23 + w = -1.145818485 Solving -0.23 + w = -1.145818485 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.23' to each side of the equation. -0.23 + 0.23 + w = -1.145818485 + 0.23 Combine like terms: -0.23 + 0.23 = 0.00 0.00 + w = -1.145818485 + 0.23 w = -1.145818485 + 0.23 Combine like terms: -1.145818485 + 0.23 = -0.915818485 w = -0.915818485 Simplifying w = -0.915818485Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.375818485, -0.915818485}
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