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Simplifying x2 + 38x + 43 = 0 Reorder the terms: 43 + 38x + x2 = 0 Solving 43 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 38x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 38x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 38x + x2 = 0 + -43 38x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 38x + x2 = -43 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = -43 + 361 Reorder the terms: 361 + 38x + x2 = -43 + 361 Combine like terms: -43 + 361 = 318 361 + 38x + x2 = 318 Factor a perfect square on the left side: (x + 19)(x + 19) = 318 Calculate the square root of the right side: 17.8325545 Break this problem into two subproblems by setting (x + 19) equal to 17.8325545 and -17.8325545.Subproblem 1
x + 19 = 17.8325545 Simplifying x + 19 = 17.8325545 Reorder the terms: 19 + x = 17.8325545 Solving 19 + x = 17.8325545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 17.8325545 + -19 Combine like terms: 19 + -19 = 0 0 + x = 17.8325545 + -19 x = 17.8325545 + -19 Combine like terms: 17.8325545 + -19 = -1.1674455 x = -1.1674455 Simplifying x = -1.1674455Subproblem 2
x + 19 = -17.8325545 Simplifying x + 19 = -17.8325545 Reorder the terms: 19 + x = -17.8325545 Solving 19 + x = -17.8325545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -17.8325545 + -19 Combine like terms: 19 + -19 = 0 0 + x = -17.8325545 + -19 x = -17.8325545 + -19 Combine like terms: -17.8325545 + -19 = -36.8325545 x = -36.8325545 Simplifying x = -36.8325545Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.1674455, -36.8325545}
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