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Simplifying x2 + 4x + -119 = 0 Reorder the terms: -119 + 4x + x2 = 0 Solving -119 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '119' to each side of the equation. -119 + 4x + 119 + x2 = 0 + 119 Reorder the terms: -119 + 119 + 4x + x2 = 0 + 119 Combine like terms: -119 + 119 = 0 0 + 4x + x2 = 0 + 119 4x + x2 = 0 + 119 Combine like terms: 0 + 119 = 119 4x + x2 = 119 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 = 119 + 4 Reorder the terms: 4 + 4x + x2 = 119 + 4 Combine like terms: 119 + 4 = 123 4 + 4x + x2 = 123 Factor a perfect square on the left side: (x + 2)(x + 2) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (x + 2) equal to 11.090536506 and -11.090536506.Subproblem 1
x + 2 = 11.090536506 Simplifying x + 2 = 11.090536506 Reorder the terms: 2 + x = 11.090536506 Solving 2 + x = 11.090536506 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 = 11.090536506 + -2 Combine like terms: 2 + -2 = 0 0 + x = 11.090536506 + -2 x = 11.090536506 + -2 Combine like terms: 11.090536506 + -2 = 9.090536506 x = 9.090536506 Simplifying x = 9.090536506Subproblem 2
x + 2 = -11.090536506 Simplifying x + 2 = -11.090536506 Reorder the terms: 2 + x = -11.090536506 Solving 2 + x = -11.090536506 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 = -11.090536506 + -2 Combine like terms: 2 + -2 = 0 0 + x = -11.090536506 + -2 x = -11.090536506 + -2 Combine like terms: -11.090536506 + -2 = -13.090536506 x = -13.090536506 Simplifying x = -13.090536506Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.090536506, -13.090536506}
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