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Simplifying 5w2 + -12w = 135 Reorder the terms: -12w + 5w2 = 135 Solving -12w + 5w2 = 135 Solving for variable 'w'. Reorder the terms: -135 + -12w + 5w2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + -12w + 5w2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -27 + -2.4w + w2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -2.4w + 27 + w2 = 0 + 27 Reorder the terms: -27 + 27 + -2.4w + w2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2.4w + w2 = 0 + 27 -2.4w + w2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2.4w + w2 = 27 The w term is -2.4w. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4w + 1.44 + w2 = 27 + 1.44 Reorder the terms: 1.44 + -2.4w + w2 = 27 + 1.44 Combine like terms: 27 + 1.44 = 28.44 1.44 + -2.4w + w2 = 28.44 Factor a perfect square on the left side: (w + -1.2)(w + -1.2) = 28.44 Calculate the square root of the right side: 5.33291665 Break this problem into two subproblems by setting (w + -1.2) equal to 5.33291665 and -5.33291665.Subproblem 1
w + -1.2 = 5.33291665 Simplifying w + -1.2 = 5.33291665 Reorder the terms: -1.2 + w = 5.33291665 Solving -1.2 + w = 5.33291665 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + w = 5.33291665 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + w = 5.33291665 + 1.2 w = 5.33291665 + 1.2 Combine like terms: 5.33291665 + 1.2 = 6.53291665 w = 6.53291665 Simplifying w = 6.53291665Subproblem 2
w + -1.2 = -5.33291665 Simplifying w + -1.2 = -5.33291665 Reorder the terms: -1.2 + w = -5.33291665 Solving -1.2 + w = -5.33291665 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + w = -5.33291665 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + w = -5.33291665 + 1.2 w = -5.33291665 + 1.2 Combine like terms: -5.33291665 + 1.2 = -4.13291665 w = -4.13291665 Simplifying w = -4.13291665Solution
The solution to the problem is based on the solutions from the subproblems. w = {6.53291665, -4.13291665}
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