Question

Consider 8x2 - 48x = -104.

Write the equation so that a = 1: x2 + __ = __

Complete the square:
x² - 6x + __ -13 + __ = __

Factor the trinomial and simplify:
(x + __ )² = __

Use the square root property of equality to solve (x-3)² = -4.
The solutions are ______.

Answer 1

Keep it simple: got this from above answer...

Answer:

Here's just the answers without all the work for easier reading.

Step-by-step explanation:

First problem answer: x2 + -6 x = -13

Second problem answer: x2 – 6x + 9 = –13 + 9

Third problem answer: (x + -3)² = -4

Fourth problem answer: 3 + 2i

Explanation:

Answer 2

`3+ 2\mathbf{i}`

`3- 2\mathbf{i}`

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=√(-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}`