For the given equation, the solutions are [tex]x = 1 \pm 2i.[/tex]
Step-by-step explanation:
Step 1:
For an equation of the form [tex]ax^{2} +bx+c=0[/tex] the solution is [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex].
Here a is the coefficient of [tex]x^{2}[/tex], b is the coefficient of x and c is the constant term.
Comparing [tex]x^{2} -2x+5=0[/tex] with [tex]ax^{2} +bx+c=0[/tex], we get that a is 1, b is -2 and c is 5.
To get the solution, we substitute the values of a, b, and c in [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex].
Step 2:
Substituting the values, we get
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(5)}}{2(1)}.[/tex]
[tex]\frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(5)}}{2(1)} = \frac{2 \pm \sqrt{4-20}}{2}.[/tex]
[tex]\frac{2 \pm \sqrt{4-20}}{2} = \frac{2 \pm \sqrt{-16}}{2}.[/tex]
[tex]\frac{2 \pm \sqrt{-16}}{2} = \frac{2}{2} \pm \frac{4(-1)}{2} = 1 \pm 2i.[/tex]
[tex]x = 1 \pm 2i.[/tex]
