For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. Solve the following equation: x^2 - 4x + 2 = 0.

Answer

The mistake is in line (5). In line (4), the expression is x = (4 ± √8) / 2. In line (5), the square root of 8 is incorrectly simplified as 4. To correct this, √8 should be simplified as √(4 * 2) = 2√2. The correct sequence of steps should be: (4) x = (4 ± √8) / 2; (5) x = (4 ± 2√2) / 2. To reach the final answer, factor out a 2 from the numerator: x = 2(2 ± √2) / 2, which simplifies to x = 2 ± √2. Therefore, the correct solutions are x = 2 + √2 and x = 2 - √2.