We want to solve the quadratic equation x^2 – 11x + 28 = 0. To do this, we’ll use the quadratic formula, which is a general method for solving quadratic equations of the form ax^2 + bx + c = 0.

The quadratic formula is:

x = (-b ± √(b^2 – 4ac)) / (2a)

In our equation, a = 1, b = -11, and c = 28. We’ll put these values into the formula:

x = (-(-11) ± √((-11)^2 – 4 * 1 * 28)) / (2 * 1)

Now, let’s break down the formula step by step:

- Calculate b^2 – 4ac: b^2 – 4ac = (-11)^2 – 4 * 1 * 28 = 121 – 112 = 9
- Substitute this result back into the formula:

x = (11 ± √9) / (2 * 1)

- Simplify the square root of 9:

x = (11 ± 3) / 2

Now, we have two possible solutions because of the “±” symbol:

- x = (11 + 3) / 2 = 14 / 2 = 7
- x = (11 – 3) / 2 = 8 / 2 = 4

So, we have found the values of x that make the equation x^2 – 11x + 28 = 0 true. The solutions are x = 7 and x = 4. These are the values of x that, when substituted into the equation, make it equal to zero.