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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 = 13.529964086 x = 13.529964086 Simplifying x = 13.529964086Subproblem 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 = -11.529964086 x = -11.529964086 Simplifying x = -11.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.529964086, -11.529964086}
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