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Simplifying x2 + 2x + -32 + 3x + 10 = 180 Reorder the terms: -32 + 10 + 2x + 3x + x2 = 180 Combine like terms: -32 + 10 = -22 -22 + 2x + 3x + x2 = 180 Combine like terms: 2x + 3x = 5x -22 + 5x + x2 = 180 Solving -22 + 5x + x2 = 180 Solving for variable 'x'. Reorder the terms: -22 + -180 + 5x + x2 = 180 + -180 Combine like terms: -22 + -180 = -202 -202 + 5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -202 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '202' to each side of the equation. -202 + 5x + 202 + x2 = 0 + 202 Reorder the terms: -202 + 202 + 5x + x2 = 0 + 202 Combine like terms: -202 + 202 = 0 0 + 5x + x2 = 0 + 202 5x + x2 = 0 + 202 Combine like terms: 0 + 202 = 202 5x + x2 = 202 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 202 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 202 + 6.25 Combine like terms: 202 + 6.25 = 208.25 6.25 + 5x + x2 = 208.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 208.25 Calculate the square root of the right side: 14.43086969 Break this problem into two subproblems by setting (x + 2.5) equal to 14.43086969 and -14.43086969.Subproblem 1
x + 2.5 = 14.43086969 Simplifying x + 2.5 = 14.43086969 Reorder the terms: 2.5 + x = 14.43086969 Solving 2.5 + x = 14.43086969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 14.43086969 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.43086969 + -2.5 x = 14.43086969 + -2.5 Combine like terms: 14.43086969 + -2.5 = 11.93086969 x = 11.93086969 Simplifying x = 11.93086969Subproblem 2
x + 2.5 = -14.43086969 Simplifying x + 2.5 = -14.43086969 Reorder the terms: 2.5 + x = -14.43086969 Solving 2.5 + x = -14.43086969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -14.43086969 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.43086969 + -2.5 x = -14.43086969 + -2.5 Combine like terms: -14.43086969 + -2.5 = -16.93086969 x = -16.93086969 Simplifying x = -16.93086969Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.93086969, -16.93086969}
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