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Simplifying 5w2 + -2w = 4 Reorder the terms: -2w + 5w2 = 4 Solving -2w + 5w2 = 4 Solving for variable 'w'. Reorder the terms: -4 + -2w + 5w2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -2w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -0.4w + w2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -0.4w + 0.8 + w2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -0.4w + w2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -0.4w + w2 = 0 + 0.8 -0.4w + w2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -0.4w + w2 = 0.8 The w term is -0.4w. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4w + 0.04 + w2 = 0.8 + 0.04 Reorder the terms: 0.04 + -0.4w + w2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + -0.4w + w2 = 0.84 Factor a perfect square on the left side: (w + -0.2)(w + -0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (w + -0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
w + -0.2 = 0.916515139 Simplifying w + -0.2 = 0.916515139 Reorder the terms: -0.2 + w = 0.916515139 Solving -0.2 + w = 0.916515139 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + w = 0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + w = 0.916515139 + 0.2 w = 0.916515139 + 0.2 Combine like terms: 0.916515139 + 0.2 = 1.116515139 w = 1.116515139 Simplifying w = 1.116515139Subproblem 2
w + -0.2 = -0.916515139 Simplifying w + -0.2 = -0.916515139 Reorder the terms: -0.2 + w = -0.916515139 Solving -0.2 + w = -0.916515139 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + w = -0.916515139 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + w = -0.916515139 + 0.2 w = -0.916515139 + 0.2 Combine like terms: -0.916515139 + 0.2 = -0.716515139 w = -0.716515139 Simplifying w = -0.716515139Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.116515139, -0.716515139}
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