Question

Consider 8x2 - 48x = -104.

Answer 1

Answer:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$

Step-by-step explanation:

Quadratic Equation Solving

We have the equation:

$8x^2-48x=-104$

Divide by 8:

$x^2-6x=-13$

Now complete the squares so the left side is a perfect square of a binomial:

$x^2-6x+9=-13+9=-4$

Factoring the perfect square:

$(x-3)^2=-4$

Taking the square root:

$x-3=\sqrt{-4}$

The square root of a negative number is an imaginary number:

$x-3=\pm 2\mathbf{i}$

Solving for x:

$x=3\pm 2\mathbf{i}$

The solutions are:

$3+ 2\mathbf{i}$

$3- 2\mathbf{i}$