The solutions to the quadratic equation x^2 + 20 = 0 are complex numbers: x1 = 2√5i and x2 = -2√5i, approximately equal to 4.47i and -4.47i, respectively.
Use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = 0, and c = 20. Substituting these values, we get:
x = (-0 ± √(0^2 - 4 * 1 * 20)) / 2 * 1
x = (± √(-80)) / 2
Simplify the expression:
x = ± √(-80)
Since the square root of a negative number is imaginary, we can express it as √-80 = 4√5i
Separate the real and imaginary parts:
x = ± (2√5i)
Therefore, the solutions are:
x1 = 2√5i
x2 = -2√5i
Decimal approximations:
x1 ≈ 4.47i
x2 ≈ -4.47i
The solutions to the equation x^2 + 20 = 0 are x1 = 2√5i and x2 = -2√5i, which can be approximated decimally as x1 ≈ 4.47i and x2 ≈ -4.47i.