Answer:
D
Step-by-step explanation:
So we have the equation:
[tex]x^2-6x+58=0[/tex]
And we want to solve for x.
We can solve it by completing the square.
First, subtract 58 from both sides:
[tex]x^2-6x=-58[/tex]
Divide the b term by 2 and square it:
[tex](-6)/2=-3\\(-3)^2=9[/tex]
So, add 9 to both sides:
[tex](x^2-6x+9)=-58+9[/tex]
On the left, the perfect square trinomial pattern. Add on the right. So:
[tex](x-3)^2=-49[/tex]
Take the square root of both sides:
[tex]x-3=\pm \sqrt{-49}[/tex]
The square root of -49 is 7i:
[tex]x-3=\pm 7i[/tex]
Add 3 to both sides:
[tex]x=3\pm 7i[/tex]
So, our answer is D.
And we're done!
