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Simplifying x2 + 2x + -112 = 0 Reorder the terms: -112 + 2x + x2 = 0 Solving -112 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '112' to each side of the equation. -112 + 2x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 2x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 2x + x2 = 0 + 112 2x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 2x + x2 = 112 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 = 112 + 1 Reorder the terms: 1 + 2x + x2 = 112 + 1 Combine like terms: 112 + 1 = 113 1 + 2x + x2 = 113 Factor a perfect square on the left side: (x + 1)(x + 1) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 1) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 1 = 10.630145813 Simplifying x + 1 = 10.630145813 Reorder the terms: 1 + x = 10.630145813 Solving 1 + x = 10.630145813 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 = 10.630145813 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.630145813 + -1 x = 10.630145813 + -1 Combine like terms: 10.630145813 + -1 = 9.630145813 x = 9.630145813 Simplifying x = 9.630145813Subproblem 2
x + 1 = -10.630145813 Simplifying x + 1 = -10.630145813 Reorder the terms: 1 + x = -10.630145813 Solving 1 + x = -10.630145813 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 = -10.630145813 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.630145813 + -1 x = -10.630145813 + -1 Combine like terms: -10.630145813 + -1 = -11.630145813 x = -11.630145813 Simplifying x = -11.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.630145813, -11.630145813}
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