Solve x^2+6x+13=0
and about time, too ...
It will not factor, since the discriminant is negative. So, use the quadratic formula.
x = (-6±√(6^2-4*13))/2 = (-6±√16 i)/2 = (-6±4i)/2 = -3±2i
Or, complete the square
x^2+6x+13 = 0
x^2+6x+9 = -4
(x+3)^2 = -4
x+3 = ±2i
x = -3±2i
This is the one I tried to answer but was told I was banned.
To solve the quadratic equation x^2 + 6x + 13 = 0, we can use the quadratic formula.
The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our given quadratic equation x^2 + 6x + 13 = 0, we have a = 1, b = 6, and c = 13.
Substituting these values into the quadratic formula, we get:
x = (-6 ± √(6^2 - 4(1)(13))) / (2(1))
Simplifying further:
x = (-6 ± √(36 - 52)) / 2
x = (-6 ± √(-16)) / 2
Since we have a negative value under the square root, the solutions to this quadratic equation involve complex numbers rather than real numbers.
Using the property of imaginary numbers, where √(-1) is denoted by "i", we can further simplify the equation:
x = (-6 ± 4i) / 2
Dividing each term by 2, we get:
x = -3 ± 2i
Therefore, the solutions to the equation x^2 + 6x + 13 = 0 are x = -3 + 2i and x = -3 - 2i.