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Simplifying 5w2 + 2w + -63 = 0 Reorder the terms: -63 + 2w + 5w2 = 0 Solving -63 + 2w + 5w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -12.6 + 0.4w + w2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 0.4w + 12.6 + w2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 0.4w + w2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 0.4w + w2 = 0 + 12.6 0.4w + w2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 0.4w + w2 = 12.6 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 = 12.6 + 0.04 Reorder the terms: 0.04 + 0.4w + w2 = 12.6 + 0.04 Combine like terms: 12.6 + 0.04 = 12.64 0.04 + 0.4w + w2 = 12.64 Factor a perfect square on the left side: (w + 0.2)(w + 0.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (w + 0.2) equal to 3.555277767 and -3.555277767.Subproblem 1
w + 0.2 = 3.555277767 Simplifying w + 0.2 = 3.555277767 Reorder the terms: 0.2 + w = 3.555277767 Solving 0.2 + w = 3.555277767 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 = 3.555277767 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = 3.555277767 + -0.2 w = 3.555277767 + -0.2 Combine like terms: 3.555277767 + -0.2 = 3.355277767 w = 3.355277767 Simplifying w = 3.355277767Subproblem 2
w + 0.2 = -3.555277767 Simplifying w + 0.2 = -3.555277767 Reorder the terms: 0.2 + w = -3.555277767 Solving 0.2 + w = -3.555277767 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 = -3.555277767 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + w = -3.555277767 + -0.2 w = -3.555277767 + -0.2 Combine like terms: -3.555277767 + -0.2 = -3.755277767 w = -3.755277767 Simplifying w = -3.755277767Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.355277767, -3.755277767}
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