Solve

x^2-6x+13=0

If the coefficient of the x^2 term is 1 and the middle term coefficient is even, I use completing the square rather than the formula

x^2 - 6x + ... = -13 + ....
x^2- 6x + 9 = -13+9
(x-3)^2 = -4
x-3 = ±√-4
x = 3 ± 2i

In google type:

quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type:

x ^ 2 - 6 x + 13 = 0

and click option: solve it!

You wil see solution step-by-step

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 of the form \(ax^2+bx+c=0\), the solutions can be found using the formula:
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

In our equation, \(x^2-6x+13=0\), we can identify the coefficients \(a=1\), \(b=-6\), and \(c=13\). Substituting these values into the quadratic formula, we get:
\[x=\frac{-(-6)\pm\sqrt{(-6)^2-4(1)(13)}}{2(1)}\]

Simplifying further:
\[x=\frac{6\pm\sqrt{36-52}}{2}\]
\[x=\frac{6\pm\sqrt{-16}}{2}\]

We can see that the term inside the square root is negative, which means that the equation has no real solutions. The solutions of this equation are complex numbers.

Therefore, the solution to the equation \(x^2-6x+13=0\) is:
\[x=\frac{6\pm\sqrt{-16}}{2}\]