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Simplifying x2 + -24 + 2x = 180 Reorder the terms: -24 + 2x + x2 = 180 Solving -24 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: -24 + -180 + 2x + x2 = 180 + -180 Combine like terms: -24 + -180 = -204 -204 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -204 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + 2x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 2x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 2x + x2 = 0 + 204 2x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 2x + x2 = 204 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 204 + 1 Reorder the terms: 1 + 2x + x2 = 204 + 1 Combine like terms: 204 + 1 = 205 1 + 2x + x2 = 205 Factor a perfect square on the left side: (x + 1)(x + 1) = 205 Calculate the square root of the right side: 14.317821063 Break this problem into two subproblems by setting (x + 1) equal to 14.317821063 and -14.317821063.Subproblem 1
x + 1 = 14.317821063 Simplifying x + 1 = 14.317821063 Reorder the terms: 1 + x = 14.317821063 Solving 1 + x = 14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 14.317821063 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.317821063 + -1 x = 14.317821063 + -1 Combine like terms: 14.317821063 + -1 = 13.317821063 x = 13.317821063 Simplifying x = 13.317821063Subproblem 2
x + 1 = -14.317821063 Simplifying x + 1 = -14.317821063 Reorder the terms: 1 + x = -14.317821063 Solving 1 + x = -14.317821063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -14.317821063 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.317821063 + -1 x = -14.317821063 + -1 Combine like terms: -14.317821063 + -1 = -15.317821063 x = -15.317821063 Simplifying x = -15.317821063Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.317821063, -15.317821063}
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