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Simplifying 3w2 + -36w + -63 = 0 Reorder the terms: -63 + -36w + 3w2 = 0 Solving -63 + -36w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -12w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + -12w + w2)' equal to zero and attempt to solve: Simplifying -21 + -12w + w2 = 0 Solving -21 + -12w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -12w + 21 + w2 = 0 + 21 Reorder the terms: -21 + 21 + -12w + w2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -12w + w2 = 0 + 21 -12w + w2 = 0 + 21 Combine like terms: 0 + 21 = 21 -12w + w2 = 21 The w term is -12w. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12w + 36 + w2 = 21 + 36 Reorder the terms: 36 + -12w + w2 = 21 + 36 Combine like terms: 21 + 36 = 57 36 + -12w + w2 = 57 Factor a perfect square on the left side: (w + -6)(w + -6) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (w + -6) equal to 7.549834435 and -7.549834435.Subproblem 1
w + -6 = 7.549834435 Simplifying w + -6 = 7.549834435 Reorder the terms: -6 + w = 7.549834435 Solving -6 + w = 7.549834435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 7.549834435 + 6 Combine like terms: -6 + 6 = 0 0 + w = 7.549834435 + 6 w = 7.549834435 + 6 Combine like terms: 7.549834435 + 6 = 13.549834435 w = 13.549834435 Simplifying w = 13.549834435Subproblem 2
w + -6 = -7.549834435 Simplifying w + -6 = -7.549834435 Reorder the terms: -6 + w = -7.549834435 Solving -6 + w = -7.549834435 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = -7.549834435 + 6 Combine like terms: -6 + 6 = 0 0 + w = -7.549834435 + 6 w = -7.549834435 + 6 Combine like terms: -7.549834435 + 6 = -1.549834435 w = -1.549834435 Simplifying w = -1.549834435Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.549834435, -1.549834435}Solution
w = {13.549834435, -1.549834435}
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