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Simplifying (w2 + 2w + -77) * 4 = 0 Reorder the terms: (-77 + 2w + w2) * 4 = 0 Reorder the terms for easier multiplication: 4(-77 + 2w + w2) = 0 (-77 * 4 + 2w * 4 + w2 * 4) = 0 (-308 + 8w + 4w2) = 0 Solving -308 + 8w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-77 + 2w + w2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-77 + 2w + w2)' equal to zero and attempt to solve: Simplifying -77 + 2w + w2 = 0 Solving -77 + 2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 2w + 77 + w2 = 0 + 77 Reorder the terms: -77 + 77 + 2w + w2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 2w + w2 = 0 + 77 2w + w2 = 0 + 77 Combine like terms: 0 + 77 = 77 2w + w2 = 77 The w term is 2w. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2w + 1 + w2 = 77 + 1 Reorder the terms: 1 + 2w + w2 = 77 + 1 Combine like terms: 77 + 1 = 78 1 + 2w + w2 = 78 Factor a perfect square on the left side: (w + 1)(w + 1) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (w + 1) equal to 8.831760866 and -8.831760866.Subproblem 1
w + 1 = 8.831760866 Simplifying w + 1 = 8.831760866 Reorder the terms: 1 + w = 8.831760866 Solving 1 + w = 8.831760866 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 8.831760866 + -1 Combine like terms: 1 + -1 = 0 0 + w = 8.831760866 + -1 w = 8.831760866 + -1 Combine like terms: 8.831760866 + -1 = 7.831760866 w = 7.831760866 Simplifying w = 7.831760866Subproblem 2
w + 1 = -8.831760866 Simplifying w + 1 = -8.831760866 Reorder the terms: 1 + w = -8.831760866 Solving 1 + w = -8.831760866 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -8.831760866 + -1 Combine like terms: 1 + -1 = 0 0 + w = -8.831760866 + -1 w = -8.831760866 + -1 Combine like terms: -8.831760866 + -1 = -9.831760866 w = -9.831760866 Simplifying w = -9.831760866Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.831760866, -9.831760866}Solution
w = {7.831760866, -9.831760866}
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