Use the quadratic formula to solve the equation:
`x^{2}-7x+6=0`
<-------SHOW YOUR WORK
To solve the equation `x^2 - 7x + 6 = 0` using the quadratic formula, we first need to identify the values of `a`, `b`, and `c` in the quadratic equation `ax^2 + bx + c = 0`.
In this case, `a = 1`, `b = -7`, and `c = 6`.
The quadratic formula is given by:
`x = (-b ± sqrt(b^2 - 4ac)) / (2a)`
Substituting the given values, we have:
`x = (-(-7) ± sqrt((-7)^2 - 4(1)(6))) / (2(1))`
Simplifying further:
`x = (7 ± sqrt(49 - 24)) / 2`
`x = (7 ± sqrt(25)) / 2`
`x = (7 ± 5) / 2`
This gives us two possible solutions:
1. `x = (7 + 5) / 2 = 12 / 2 = 6`
2. `x = (7 - 5) / 2 = 2 / 2 = 1`
Therefore, the solutions to the equation `x^2 - 7x + 6 = 0` are `x = 6` and `x = 1`.