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Simplifying x(x + 2) = 146 Reorder the terms: x(2 + x) = 146 (2 * x + x * x) = 146 (2x + x2) = 146 Solving 2x + x2 = 146 Solving for variable 'x'. Reorder the terms: -146 + 2x + x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -146 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + 2x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + 2x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + 2x + x2 = 0 + 146 2x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 2x + x2 = 146 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 = 146 + 1 Reorder the terms: 1 + 2x + x2 = 146 + 1 Combine like terms: 146 + 1 = 147 1 + 2x + x2 = 147 Factor a perfect square on the left side: (x + 1)(x + 1) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (x + 1) equal to 12.124355653 and -12.124355653.Subproblem 1
x + 1 = 12.124355653 Simplifying x + 1 = 12.124355653 Reorder the terms: 1 + x = 12.124355653 Solving 1 + x = 12.124355653 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 = 12.124355653 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.124355653 + -1 x = 12.124355653 + -1 Combine like terms: 12.124355653 + -1 = 11.124355653 x = 11.124355653 Simplifying x = 11.124355653Subproblem 2
x + 1 = -12.124355653 Simplifying x + 1 = -12.124355653 Reorder the terms: 1 + x = -12.124355653 Solving 1 + x = -12.124355653 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 = -12.124355653 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.124355653 + -1 x = -12.124355653 + -1 Combine like terms: -12.124355653 + -1 = -13.124355653 x = -13.124355653 Simplifying x = -13.124355653Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.124355653, -13.124355653}
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