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Simplifying x2 + 38x = 67 Reorder the terms: 38x + x2 = 67 Solving 38x + x2 = 67 Solving for variable 'x'. Reorder the terms: -67 + 38x + x2 = 67 + -67 Combine like terms: 67 + -67 = 0 -67 + 38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + 38x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + 38x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + 38x + x2 = 0 + 67 38x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 38x + x2 = 67 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 = 67 + 361 Reorder the terms: 361 + 38x + x2 = 67 + 361 Combine like terms: 67 + 361 = 428 361 + 38x + x2 = 428 Factor a perfect square on the left side: (x + 19)(x + 19) = 428 Calculate the square root of the right side: 20.688160866 Break this problem into two subproblems by setting (x + 19) equal to 20.688160866 and -20.688160866.Subproblem 1
x + 19 = 20.688160866 Simplifying x + 19 = 20.688160866 Reorder the terms: 19 + x = 20.688160866 Solving 19 + x = 20.688160866 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 = 20.688160866 + -19 Combine like terms: 19 + -19 = 0 0 + x = 20.688160866 + -19 x = 20.688160866 + -19 Combine like terms: 20.688160866 + -19 = 1.688160866 x = 1.688160866 Simplifying x = 1.688160866Subproblem 2
x + 19 = -20.688160866 Simplifying x + 19 = -20.688160866 Reorder the terms: 19 + x = -20.688160866 Solving 19 + x = -20.688160866 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 = -20.688160866 + -19 Combine like terms: 19 + -19 = 0 0 + x = -20.688160866 + -19 x = -20.688160866 + -19 Combine like terms: -20.688160866 + -19 = -39.688160866 x = -39.688160866 Simplifying x = -39.688160866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.688160866, -39.688160866}
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