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Simplifying -3w2 + 42w + 111 = 0 Reorder the terms: 111 + 42w + -3w2 = 0 Solving 111 + 42w + -3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(37 + 14w + -1w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(37 + 14w + -1w2)' equal to zero and attempt to solve: Simplifying 37 + 14w + -1w2 = 0 Solving 37 + 14w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -37 + -14w + w2 = 0 Move the constant term to the right: Add '37' to each side of the equation. -37 + -14w + 37 + w2 = 0 + 37 Reorder the terms: -37 + 37 + -14w + w2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -14w + w2 = 0 + 37 -14w + w2 = 0 + 37 Combine like terms: 0 + 37 = 37 -14w + w2 = 37 The w term is -14w. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14w + 49 + w2 = 37 + 49 Reorder the terms: 49 + -14w + w2 = 37 + 49 Combine like terms: 37 + 49 = 86 49 + -14w + w2 = 86 Factor a perfect square on the left side: (w + -7)(w + -7) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (w + -7) equal to 9.273618495 and -9.273618495.Subproblem 1
w + -7 = 9.273618495 Simplifying w + -7 = 9.273618495 Reorder the terms: -7 + w = 9.273618495 Solving -7 + w = 9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + w = 9.273618495 + 7 Combine like terms: -7 + 7 = 0 0 + w = 9.273618495 + 7 w = 9.273618495 + 7 Combine like terms: 9.273618495 + 7 = 16.273618495 w = 16.273618495 Simplifying w = 16.273618495Subproblem 2
w + -7 = -9.273618495 Simplifying w + -7 = -9.273618495 Reorder the terms: -7 + w = -9.273618495 Solving -7 + w = -9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + w = -9.273618495 + 7 Combine like terms: -7 + 7 = 0 0 + w = -9.273618495 + 7 w = -9.273618495 + 7 Combine like terms: -9.273618495 + 7 = -2.273618495 w = -2.273618495 Simplifying w = -2.273618495Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.273618495, -2.273618495}Solution
w = {16.273618495, -2.273618495}
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