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Simplifying x2 + 2x + -156 = 0 Reorder the terms: -156 + 2x + x2 = 0 Solving -156 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + 2x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + 2x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 2x + x2 = 0 + 156 2x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 2x + x2 = 156 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 = 156 + 1 Reorder the terms: 1 + 2x + x2 = 156 + 1 Combine like terms: 156 + 1 = 157 1 + 2x + x2 = 157 Factor a perfect square on the left side: (x + 1)(x + 1) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 1) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 1 = 12.529964086 Simplifying x + 1 = 12.529964086 Reorder the terms: 1 + x = 12.529964086 Solving 1 + x = 12.529964086 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 = 12.529964086 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.529964086 + -1 x = 12.529964086 + -1 Combine like terms: 12.529964086 + -1 = 11.529964086 x = 11.529964086 Simplifying x = 11.529964086Subproblem 2
x + 1 = -12.529964086 Simplifying x + 1 = -12.529964086 Reorder the terms: 1 + x = -12.529964086 Solving 1 + x = -12.529964086 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 = -12.529964086 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.529964086 + -1 x = -12.529964086 + -1 Combine like terms: -12.529964086 + -1 = -13.529964086 x = -13.529964086 Simplifying x = -13.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.529964086, -13.529964086}
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