(x-4)2+8=0 In Standard

2 min read Jun 17, 2024

Solving the Quadratic Equation (x-4)² + 8 = 0

This equation is a quadratic equation because it has a term with a variable raised to the power of 2. Let's break down the steps to solve it:

First, we need to expand the squared term:

(x-4)² = (x-4)(x-4) = x² - 8x + 16

Now, our equation becomes:

x² - 8x + 16 + 8 = 0

Combining the constant terms, we get:

x² - 8x + 24 = 0

The quadratic formula is a general solution for equations of the form ax² + bx + c = 0:

x = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 1, b = -8, and c = 24. Plugging these values into the formula:

x = (8 ± √((-8)² - 4 * 1 * 24)) / (2 * 1)

Simplifying the equation:

x = (8 ± √(64 - 96)) / 2 x = (8 ± √(-32)) / 2 x = (8 ± 4√(-2)) / 2

Since the square root of a negative number is imaginary, we can write:

x = (8 ± 4i√2) / 2

Where 'i' represents the imaginary unit, √-1.

Finally, simplifying further:

x = 4 ± 2i√2

Therefore, the solutions to the equation (x-4)² + 8 = 0 are:

These solutions are complex numbers, with both a real part (4) and an imaginary part (2√2).