x^{2}-4x-21=0

Answer 1

To solve the quadratic equation x^2 - 4x - 21 = 0, we can factor the equation or use the quadratic formula.

Factoring:
x^2 - 4x - 21 = 0
(x - 7)(x + 3) = 0
So, the solutions are x = 7 and x = -3.

Using the Quadratic Formula:
For the quadratic equation ax^2 + bx + c = 0, the solutions can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = -4, and c = -21:
x = (4 ± √((-4)^2 - 4*1*(-21))) / 2*1
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2

This gives us two solutions:
x = (4 + 10) / 2 = 14 / 2 = 7
x = (4 - 10) / 2 = -6 / 2 = -3

Therefore, the solutions to the quadratic equation x^2 - 4x - 21 = 0 are x = 7 and x = -3.