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Simplifying (5w * w) + 4 = w + 6 Multiply w * w (5w2) + 4 = w + 6 Reorder the terms: 4 + (5w2) = w + 6 Reorder the terms: 4 + (5w2) = 6 + w Solving 4 + (5w2) = 6 + w Solving for variable 'w'. Reorder the terms: 4 + -6 + -1w + (5w2) = 6 + w + -6 + -1w Combine like terms: 4 + -6 = -2 -2 + -1w + (5w2) = 6 + w + -6 + -1w Reorder the terms: -2 + -1w + (5w2) = 6 + -6 + w + -1w Combine like terms: 6 + -6 = 0 -2 + -1w + (5w2) = 0 + w + -1w -2 + -1w + (5w2) = w + -1w Combine like terms: w + -1w = 0 -2 + -1w + (5w2) = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -0.2w + w2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -0.2w + 0.4 + w2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -0.2w + w2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -0.2w + w2 = 0 + 0.4 -0.2w + w2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -0.2w + w2 = 0.4 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 = 0.4 + 0.01 Reorder the terms: 0.01 + -0.2w + w2 = 0.4 + 0.01 Combine like terms: 0.4 + 0.01 = 0.41 0.01 + -0.2w + w2 = 0.41 Factor a perfect square on the left side: ((w) + -0.1)((w) + -0.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting ((w) + -0.1) equal to 0.640312424 and -0.640312424.Subproblem 1
(w) + -0.1 = 0.640312424 Simplifying (w) + -0.1 = 0.640312424 w + -0.1 = 0.640312424 Reorder the terms: -0.1 + w = 0.640312424 Solving -0.1 + w = 0.640312424 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 = 0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + w = 0.640312424 + 0.1 w = 0.640312424 + 0.1 Combine like terms: 0.640312424 + 0.1 = 0.740312424 w = 0.740312424 Simplifying w = 0.740312424Subproblem 2
(w) + -0.1 = -0.640312424 Simplifying (w) + -0.1 = -0.640312424 w + -0.1 = -0.640312424 Reorder the terms: -0.1 + w = -0.640312424 Solving -0.1 + w = -0.640312424 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 = -0.640312424 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + w = -0.640312424 + 0.1 w = -0.640312424 + 0.1 Combine like terms: -0.640312424 + 0.1 = -0.540312424 w = -0.540312424 Simplifying w = -0.540312424Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.740312424, -0.540312424}
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