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Simplifying x2 + 22x + -36 = 0 Reorder the terms: -36 + 22x + x2 = 0 Solving -36 + 22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 22x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 22x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 22x + x2 = 0 + 36 22x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 22x + x2 = 36 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 36 + 121 Reorder the terms: 121 + 22x + x2 = 36 + 121 Combine like terms: 36 + 121 = 157 121 + 22x + x2 = 157 Factor a perfect square on the left side: (x + 11)(x + 11) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (x + 11) equal to 12.529964086 and -12.529964086.Subproblem 1
x + 11 = 12.529964086 Simplifying x + 11 = 12.529964086 Reorder the terms: 11 + x = 12.529964086 Solving 11 + x = 12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 12.529964086 + -11 Combine like terms: 11 + -11 = 0 0 + x = 12.529964086 + -11 x = 12.529964086 + -11 Combine like terms: 12.529964086 + -11 = 1.529964086 x = 1.529964086 Simplifying x = 1.529964086Subproblem 2
x + 11 = -12.529964086 Simplifying x + 11 = -12.529964086 Reorder the terms: 11 + x = -12.529964086 Solving 11 + x = -12.529964086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -12.529964086 + -11 Combine like terms: 11 + -11 = 0 0 + x = -12.529964086 + -11 x = -12.529964086 + -11 Combine like terms: -12.529964086 + -11 = -23.529964086 x = -23.529964086 Simplifying x = -23.529964086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.529964086, -23.529964086}
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