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Simplifying 25w2 + -20w = 4 Reorder the terms: -20w + 25w2 = 4 Solving -20w + 25w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + -20w + 25w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -20w + 25w2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -0.8w + w2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.8w + 0.16 + w2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.8w + w2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.8w + w2 = 0 + 0.16 -0.8w + w2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.8w + w2 = 0.16 The w term is -0.8w. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8w + 0.16 + w2 = 0.16 + 0.16 Reorder the terms: 0.16 + -0.8w + w2 = 0.16 + 0.16 Combine like terms: 0.16 + 0.16 = 0.32 0.16 + -0.8w + w2 = 0.32 Factor a perfect square on the left side: (w + -0.4)(w + -0.4) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (w + -0.4) equal to 0.565685425 and -0.565685425.Subproblem 1
w + -0.4 = 0.565685425 Simplifying w + -0.4 = 0.565685425 Reorder the terms: -0.4 + w = 0.565685425 Solving -0.4 + w = 0.565685425 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = 0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = 0.565685425 + 0.4 w = 0.565685425 + 0.4 Combine like terms: 0.565685425 + 0.4 = 0.965685425 w = 0.965685425 Simplifying w = 0.965685425Subproblem 2
w + -0.4 = -0.565685425 Simplifying w + -0.4 = -0.565685425 Reorder the terms: -0.4 + w = -0.565685425 Solving -0.4 + w = -0.565685425 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = -0.565685425 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = -0.565685425 + 0.4 w = -0.565685425 + 0.4 Combine like terms: -0.565685425 + 0.4 = -0.165685425 w = -0.165685425 Simplifying w = -0.165685425Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.965685425, -0.165685425}
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