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Simplifying x2 + 2x + -3 + x2 + 3x + -8 = 180 Reorder the terms: -3 + -8 + 2x + 3x + x2 + x2 = 180 Combine like terms: -3 + -8 = -11 -11 + 2x + 3x + x2 + x2 = 180 Combine like terms: 2x + 3x = 5x -11 + 5x + x2 + x2 = 180 Combine like terms: x2 + x2 = 2x2 -11 + 5x + 2x2 = 180 Solving -11 + 5x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -11 + -180 + 5x + 2x2 = 180 + -180 Combine like terms: -11 + -180 = -191 -191 + 5x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -191 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -95.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '95.5' to each side of the equation. -95.5 + 2.5x + 95.5 + x2 = 0 + 95.5 Reorder the terms: -95.5 + 95.5 + 2.5x + x2 = 0 + 95.5 Combine like terms: -95.5 + 95.5 = 0.0 0.0 + 2.5x + x2 = 0 + 95.5 2.5x + x2 = 0 + 95.5 Combine like terms: 0 + 95.5 = 95.5 2.5x + x2 = 95.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 95.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 95.5 + 1.5625 Combine like terms: 95.5 + 1.5625 = 97.0625 1.5625 + 2.5x + x2 = 97.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 97.0625 Calculate the square root of the right side: 9.852030248 Break this problem into two subproblems by setting (x + 1.25) equal to 9.852030248 and -9.852030248.Subproblem 1
x + 1.25 = 9.852030248 Simplifying x + 1.25 = 9.852030248 Reorder the terms: 1.25 + x = 9.852030248 Solving 1.25 + x = 9.852030248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 9.852030248 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.852030248 + -1.25 x = 9.852030248 + -1.25 Combine like terms: 9.852030248 + -1.25 = 8.602030248 x = 8.602030248 Simplifying x = 8.602030248Subproblem 2
x + 1.25 = -9.852030248 Simplifying x + 1.25 = -9.852030248 Reorder the terms: 1.25 + x = -9.852030248 Solving 1.25 + x = -9.852030248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -9.852030248 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.852030248 + -1.25 x = -9.852030248 + -1.25 Combine like terms: -9.852030248 + -1.25 = -11.102030248 x = -11.102030248 Simplifying x = -11.102030248Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.602030248, -11.102030248}
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