Answer: x = 3 ± 4i
Step-by-step explanation:
x² - 6x + 25 = 0
a=1 b= -6 c=25
Use Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]= \frac{-(-6) +/- \sqrt{(-6)^{2}-4(1)(25)}}{2(1)}[/tex]
[tex]= \frac{6 +/- \sqrt{36-100}}{2}[/tex]
[tex]= \frac{6 +/- \sqrt{-64}}{2}[/tex]
[tex]= \frac{6 +/- 8i}{2}[/tex]
[tex]= \frac{2(3 +/- 4i)}{2}[/tex]
= 3 ± 4i
Answer:
x= 3+4i , x= 3-4i
Step-by-step explanation:
x^2-6x= -25
To solve for x we need to make right hand side
So add 25 on both sides
[tex]x^2-6x+25=0[/tex]
Now apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
From the given equation a=1, b=-6 and c=25
Plug in all the values in the formula
[tex]x=\frac{-(-6)+-\sqrt{(-6)^2-4(1)(25)}}{2(1)}[/tex]
[tex]x=\frac{6+-\sqrt{-64}}{2}[/tex]
We know [tex]\sqrt{-1} =i[/tex]
So equation becomes
[tex]x=\frac{6+8i}{2}[/tex]
Divide by 2
x= 3+-4i
So x= 3+4i , x= 3-4i
