To solve the expression x² + 8x + 20, we first need to find the values of x that will satisfy the equation. This expression is a quadratic equation in the form of ax² + bx + c, where:
- a = 1
- b = 8
- c = 20
We can use the quadratic formula to find the roots, which states:
x = (-b ± √(b² – 4ac)) / 2a
Substituting the values of a, b, and c into the formula:
x = (-8 ± √(8² – 4 * 1 * 20)) / (2 * 1)
This simplifies to:
x = (-8 ± √(64 – 80)) / 2
x = (-8 ± √(-16)) / 2
At this point, we see that the term under the square root (-16) is negative, indicating that the roots are complex. To express the roots, we can write:
√(-16) = 4i (where i is the imaginary unit).
So the solutions become:
x = (-8 ± 4i) / 2
This simplifies to:
x = -4 ± 2i
Thus, the solutions to the equation x² + 8x + 20 = 0 are:
- x = -4 + 2i
- x = -4 – 2i
In conclusion, since the discriminant is negative, the equation does not have real roots but instead has two complex roots.