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Simplifying x2 + 4x + -121 = 0 Reorder the terms: -121 + 4x + x2 = 0 Solving -121 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + 4x + 121 + x2 = 0 + 121 Reorder the terms: -121 + 121 + 4x + x2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + 4x + x2 = 0 + 121 4x + x2 = 0 + 121 Combine like terms: 0 + 121 = 121 4x + x2 = 121 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 121 + 4 Reorder the terms: 4 + 4x + x2 = 121 + 4 Combine like terms: 121 + 4 = 125 4 + 4x + x2 = 125 Factor a perfect square on the left side: (x + 2)(x + 2) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 2) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 2 = 11.180339887 Simplifying x + 2 = 11.180339887 Reorder the terms: 2 + x = 11.180339887 Solving 2 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 11.180339887 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.180339887 + -2 x = 11.180339887 + -2 Combine like terms: 11.180339887 + -2 = 9.180339887 x = 9.180339887 Simplifying x = 9.180339887Subproblem 2
x + 2 = -11.180339887 Simplifying x + 2 = -11.180339887 Reorder the terms: 2 + x = -11.180339887 Solving 2 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -11.180339887 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.180339887 + -2 x = -11.180339887 + -2 Combine like terms: -11.180339887 + -2 = -13.180339887 x = -13.180339887 Simplifying x = -13.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.180339887, -13.180339887}
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