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Simplifying 4x + 5 + x2 + -27 = 180 Reorder the terms: 5 + -27 + 4x + x2 = 180 Combine like terms: 5 + -27 = -22 -22 + 4x + x2 = 180 Solving -22 + 4x + x2 = 180 Solving for variable 'x'. Reorder the terms: -22 + -180 + 4x + x2 = 180 + -180 Combine like terms: -22 + -180 = -202 -202 + 4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -202 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '202' to each side of the equation. -202 + 4x + 202 + x2 = 0 + 202 Reorder the terms: -202 + 202 + 4x + x2 = 0 + 202 Combine like terms: -202 + 202 = 0 0 + 4x + x2 = 0 + 202 4x + x2 = 0 + 202 Combine like terms: 0 + 202 = 202 4x + x2 = 202 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 202 + 4 Reorder the terms: 4 + 4x + x2 = 202 + 4 Combine like terms: 202 + 4 = 206 4 + 4x + x2 = 206 Factor a perfect square on the left side: (x + 2)(x + 2) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (x + 2) equal to 14.352700094 and -14.352700094.Subproblem 1
x + 2 = 14.352700094 Simplifying x + 2 = 14.352700094 Reorder the terms: 2 + x = 14.352700094 Solving 2 + x = 14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 14.352700094 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.352700094 + -2 x = 14.352700094 + -2 Combine like terms: 14.352700094 + -2 = 12.352700094 x = 12.352700094 Simplifying x = 12.352700094Subproblem 2
x + 2 = -14.352700094 Simplifying x + 2 = -14.352700094 Reorder the terms: 2 + x = -14.352700094 Solving 2 + x = -14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -14.352700094 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.352700094 + -2 x = -14.352700094 + -2 Combine like terms: -14.352700094 + -2 = -16.352700094 x = -16.352700094 Simplifying x = -16.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.352700094, -16.352700094}
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