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Simplifying x2 + 2x + 114 = 180 Reorder the terms: 114 + 2x + x2 = 180 Solving 114 + 2x + x2 = 180 Solving for variable 'x'. Reorder the terms: 114 + -180 + 2x + x2 = 180 + -180 Combine like terms: 114 + -180 = -66 -66 + 2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -66 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 2x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 2x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 2x + x2 = 0 + 66 2x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 2x + x2 = 66 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 = 66 + 1 Reorder the terms: 1 + 2x + x2 = 66 + 1 Combine like terms: 66 + 1 = 67 1 + 2x + x2 = 67 Factor a perfect square on the left side: (x + 1)(x + 1) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 1) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 1 = 8.185352772 Simplifying x + 1 = 8.185352772 Reorder the terms: 1 + x = 8.185352772 Solving 1 + x = 8.185352772 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 = 8.185352772 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.185352772 + -1 x = 8.185352772 + -1 Combine like terms: 8.185352772 + -1 = 7.185352772 x = 7.185352772 Simplifying x = 7.185352772Subproblem 2
x + 1 = -8.185352772 Simplifying x + 1 = -8.185352772 Reorder the terms: 1 + x = -8.185352772 Solving 1 + x = -8.185352772 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 = -8.185352772 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.185352772 + -1 x = -8.185352772 + -1 Combine like terms: -8.185352772 + -1 = -9.185352772 x = -9.185352772 Simplifying x = -9.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.185352772, -9.185352772}
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