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Simplifying 4x2 + 114x + 11 = 180 Reorder the terms: 11 + 114x + 4x2 = 180 Solving 11 + 114x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 11 + -180 + 114x + 4x2 = 180 + -180 Combine like terms: 11 + -180 = -169 -169 + 114x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -169 + 114x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -42.25 + 28.5x + x2 = 0 Move the constant term to the right: Add '42.25' to each side of the equation. -42.25 + 28.5x + 42.25 + x2 = 0 + 42.25 Reorder the terms: -42.25 + 42.25 + 28.5x + x2 = 0 + 42.25 Combine like terms: -42.25 + 42.25 = 0.00 0.00 + 28.5x + x2 = 0 + 42.25 28.5x + x2 = 0 + 42.25 Combine like terms: 0 + 42.25 = 42.25 28.5x + x2 = 42.25 The x term is 28.5x. Take half its coefficient (14.25). Square it (203.0625) and add it to both sides. Add '203.0625' to each side of the equation. 28.5x + 203.0625 + x2 = 42.25 + 203.0625 Reorder the terms: 203.0625 + 28.5x + x2 = 42.25 + 203.0625 Combine like terms: 42.25 + 203.0625 = 245.3125 203.0625 + 28.5x + x2 = 245.3125 Factor a perfect square on the left side: (x + 14.25)(x + 14.25) = 245.3125 Calculate the square root of the right side: 15.662455108 Break this problem into two subproblems by setting (x + 14.25) equal to 15.662455108 and -15.662455108.Subproblem 1
x + 14.25 = 15.662455108 Simplifying x + 14.25 = 15.662455108 Reorder the terms: 14.25 + x = 15.662455108 Solving 14.25 + x = 15.662455108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = 15.662455108 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = 15.662455108 + -14.25 x = 15.662455108 + -14.25 Combine like terms: 15.662455108 + -14.25 = 1.412455108 x = 1.412455108 Simplifying x = 1.412455108Subproblem 2
x + 14.25 = -15.662455108 Simplifying x + 14.25 = -15.662455108 Reorder the terms: 14.25 + x = -15.662455108 Solving 14.25 + x = -15.662455108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.25' to each side of the equation. 14.25 + -14.25 + x = -15.662455108 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + x = -15.662455108 + -14.25 x = -15.662455108 + -14.25 Combine like terms: -15.662455108 + -14.25 = -29.912455108 x = -29.912455108 Simplifying x = -29.912455108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.412455108, -29.912455108}
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