To solve the quadratic equation x^2 – 11x + 28 = 0, you can use the quadratic formula, which is given by:
x = (-b ± √(b^2 – 4ac)) / (2a)
In this equation, a = 1, b = -11, and c = 28. Plugging these values into the formula:
x = (-(-11) ± √((-11)^2 – 4(1)(28))) / (2(1))
x = (11 ± √(121 – 112)) / 2
x = (11 ± √9) / 2
Now, simplify further:
x = (11 ± 3) / 2
This gives you two possible solutions:
- x = (11 + 3) / 2 = 14 / 2 = 7
- x = (11 – 3) / 2 = 8 / 2 = 4
So, the solutions to the equation x^2 – 11x + 28 = 0 are x = 7 and x = 4.