Final answer:
The solution to the equation x² - 7x = -5 is x = (7 ± √(29))/2.
Step-by-step explanation:
To find the solution of the equation x² - 7x = -5, we can rearrange the equation to get x² - 7x + 5 = 0. This is a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = -7, and c = 5. We can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / (2a)
Substituting the values into the quadratic formula:
x = (-(-7) ± √((-7)² - 4(1)(5))) / (2(1))
x = (7 ± √(49 - 20)) / 2
x = (7 ± √(29)) / 2
Therefore, the solution to the equation is x = (7 ± √(29))/2.