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Simplifying x(1 + x) + (2 + x) = 228 (1 * x + x * x) + (2 + x) = 228 (1x + x2) + (2 + x) = 228 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 228 Reorder the terms: 2 + 1x + x + x2 = 228 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 228 Solving 2 + 2x + x2 = 228 Solving for variable 'x'. Reorder the terms: 2 + -228 + 2x + x2 = 228 + -228 Combine like terms: 2 + -228 = -226 -226 + 2x + x2 = 228 + -228 Combine like terms: 228 + -228 = 0 -226 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '226' to each side of the equation. -226 + 2x + 226 + x2 = 0 + 226 Reorder the terms: -226 + 226 + 2x + x2 = 0 + 226 Combine like terms: -226 + 226 = 0 0 + 2x + x2 = 0 + 226 2x + x2 = 0 + 226 Combine like terms: 0 + 226 = 226 2x + x2 = 226 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 = 226 + 1 Reorder the terms: 1 + 2x + x2 = 226 + 1 Combine like terms: 226 + 1 = 227 1 + 2x + x2 = 227 Factor a perfect square on the left side: (x + 1)(x + 1) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (x + 1) equal to 15.066519173 and -15.066519173.Subproblem 1
x + 1 = 15.066519173 Simplifying x + 1 = 15.066519173 Reorder the terms: 1 + x = 15.066519173 Solving 1 + x = 15.066519173 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 = 15.066519173 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.066519173 + -1 x = 15.066519173 + -1 Combine like terms: 15.066519173 + -1 = 14.066519173 x = 14.066519173 Simplifying x = 14.066519173Subproblem 2
x + 1 = -15.066519173 Simplifying x + 1 = -15.066519173 Reorder the terms: 1 + x = -15.066519173 Solving 1 + x = -15.066519173 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 = -15.066519173 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.066519173 + -1 x = -15.066519173 + -1 Combine like terms: -15.066519173 + -1 = -16.066519173 x = -16.066519173 Simplifying x = -16.066519173Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.066519173, -16.066519173}
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