Final answer:
The correct solution for the equation x² - 7x = -5 is x = (7 + √29) / 2, which resembles option B) 7 + √29 if the division by 2 is implied. The options are evaluated using the quadratic formula, with (7 + √29) / 2 being the right solution, and none of the other options are solutions to the given equation.
Step-by-step explanation:
The student asked which of the following is a solution of x² - 7x = -5: A) 10, B) 7 + √29, C) 2, D) -7 + √169. To solve this, we first transform the equation into standard quadratic form by adding 5 to both sides: x² - 7x + 5 = 0.
Next, we use the quadratic formula x = (-b ± √(b² - 4ac)) / (2a) with a = 1, b = -7, and c = 5:
x = (-(-7) ± √((-7)² - 4 * 1 * 5)) / (2 * 1)
x = (7 ± √(49 - 20)) / 2
x = (7 ± √29) / 2
The two possible solutions are x = (7 + √29) / 2 and x = (7 - √29) / 2. Comparing these solutions with the options given, option B) 7 + √29 could be the correct solution if the student meant (7 + √29) / 2. To verify, we need to substitute option B into the original equation and check if it satisfies the equation. Unfortunately, option D) -7 + √169, which simplifies to -7 + 13 = 6, is incorrect as 6 is not a solution to the original equation x² - 7x = -5.