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Simplifying x2 + 2x + -119 = 0 Reorder the terms: -119 + 2x + x2 = 0 Solving -119 + 2x + 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 + 2x + 119 + x2 = 0 + 119 Reorder the terms: -119 + 119 + 2x + x2 = 0 + 119 Combine like terms: -119 + 119 = 0 0 + 2x + x2 = 0 + 119 2x + x2 = 0 + 119 Combine like terms: 0 + 119 = 119 2x + x2 = 119 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 = 119 + 1 Reorder the terms: 1 + 2x + x2 = 119 + 1 Combine like terms: 119 + 1 = 120 1 + 2x + x2 = 120 Factor a perfect square on the left side: (x + 1)(x + 1) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + 1) equal to 10.95445115 and -10.95445115.Subproblem 1
x + 1 = 10.95445115 Simplifying x + 1 = 10.95445115 Reorder the terms: 1 + x = 10.95445115 Solving 1 + x = 10.95445115 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 = 10.95445115 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.95445115 + -1 x = 10.95445115 + -1 Combine like terms: 10.95445115 + -1 = 9.95445115 x = 9.95445115 Simplifying x = 9.95445115Subproblem 2
x + 1 = -10.95445115 Simplifying x + 1 = -10.95445115 Reorder the terms: 1 + x = -10.95445115 Solving 1 + x = -10.95445115 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 = -10.95445115 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.95445115 + -1 x = -10.95445115 + -1 Combine like terms: -10.95445115 + -1 = -11.95445115 x = -11.95445115 Simplifying x = -11.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.95445115, -11.95445115}
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