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Simplifying x2 + 2x = 113 Reorder the terms: 2x + x2 = 113 Solving 2x + x2 = 113 Solving for variable 'x'. Reorder the terms: -113 + 2x + x2 = 113 + -113 Combine like terms: 113 + -113 = 0 -113 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + 2x + 113 + x2 = 0 + 113 Reorder the terms: -113 + 113 + 2x + x2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + 2x + x2 = 0 + 113 2x + x2 = 0 + 113 Combine like terms: 0 + 113 = 113 2x + x2 = 113 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 = 113 + 1 Reorder the terms: 1 + 2x + x2 = 113 + 1 Combine like terms: 113 + 1 = 114 1 + 2x + x2 = 114 Factor a perfect square on the left side: (x + 1)(x + 1) = 114 Calculate the square root of the right side: 10.677078252 Break this problem into two subproblems by setting (x + 1) equal to 10.677078252 and -10.677078252.Subproblem 1
x + 1 = 10.677078252 Simplifying x + 1 = 10.677078252 Reorder the terms: 1 + x = 10.677078252 Solving 1 + x = 10.677078252 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 = 10.677078252 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.677078252 + -1 x = 10.677078252 + -1 Combine like terms: 10.677078252 + -1 = 9.677078252 x = 9.677078252 Simplifying x = 9.677078252Subproblem 2
x + 1 = -10.677078252 Simplifying x + 1 = -10.677078252 Reorder the terms: 1 + x = -10.677078252 Solving 1 + x = -10.677078252 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 = -10.677078252 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.677078252 + -1 x = -10.677078252 + -1 Combine like terms: -10.677078252 + -1 = -11.677078252 x = -11.677078252 Simplifying x = -11.677078252Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.677078252, -11.677078252}
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