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Simplifying -4w2 + 32w = -196 Reorder the terms: 32w + -4w2 = -196 Solving 32w + -4w2 = -196 Solving for variable 'w'. Reorder the terms: 196 + 32w + -4w2 = -196 + 196 Combine like terms: -196 + 196 = 0 196 + 32w + -4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(49 + 8w + -1w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(49 + 8w + -1w2)' equal to zero and attempt to solve: Simplifying 49 + 8w + -1w2 = 0 Solving 49 + 8w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + -8w + w2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + -8w + 49 + w2 = 0 + 49 Reorder the terms: -49 + 49 + -8w + w2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -8w + w2 = 0 + 49 -8w + w2 = 0 + 49 Combine like terms: 0 + 49 = 49 -8w + w2 = 49 The w term is -8w. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8w + 16 + w2 = 49 + 16 Reorder the terms: 16 + -8w + w2 = 49 + 16 Combine like terms: 49 + 16 = 65 16 + -8w + w2 = 65 Factor a perfect square on the left side: (w + -4)(w + -4) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (w + -4) equal to 8.062257748 and -8.062257748.Subproblem 1
w + -4 = 8.062257748 Simplifying w + -4 = 8.062257748 Reorder the terms: -4 + w = 8.062257748 Solving -4 + w = 8.062257748 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + w = 8.062257748 + 4 w = 8.062257748 + 4 Combine like terms: 8.062257748 + 4 = 12.062257748 w = 12.062257748 Simplifying w = 12.062257748Subproblem 2
w + -4 = -8.062257748 Simplifying w + -4 = -8.062257748 Reorder the terms: -4 + w = -8.062257748 Solving -4 + w = -8.062257748 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -8.062257748 + 4 Combine like terms: -4 + 4 = 0 0 + w = -8.062257748 + 4 w = -8.062257748 + 4 Combine like terms: -8.062257748 + 4 = -4.062257748 w = -4.062257748 Simplifying w = -4.062257748Solution
The solution to the problem is based on the solutions from the subproblems. w = {12.062257748, -4.062257748}Solution
w = {12.062257748, -4.062257748}
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