Answer:
[tex]3+ 2\mathbf{i}[/tex]
[tex]3- 2\mathbf{i}[/tex]
Step-by-step explanation:
Quadratic Equation Solving
We have the equation:
[tex]8x^2-48x=-104[/tex]
Divide by 8:
[tex]x^2-6x=-13[/tex]
Now complete the squares so the left side is a perfect square of a binomial:
[tex]x^2-6x+9=-13+9=-4[/tex]
Factoring the perfect square:
[tex](x-3)^2=-4[/tex]
Taking the square root:
[tex]x-3=\sqrt{-4}[/tex]
The square root of a negative number is an imaginary number:
[tex]x-3=\pm 2\mathbf{i}[/tex]
Solving for x:
[tex]x=3\pm 2\mathbf{i}[/tex]
The solutions are:
[tex]3+ 2\mathbf{i}[/tex]
[tex]3- 2\mathbf{i}[/tex]
