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

Jasonbradley

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Jun 17, 2024

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Solving Quadratic Equations: (x-4)² + 8 = 0

This equation represents a quadratic equation, meaning it has a highest power of 2 for the variable x. Let's break down how to solve it and present it in standard form.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation is:

ax² + bx + c = 0

where a, b, and c are coefficients, and a ≠ 0.

Transforming the Equation

Our current equation is (x-4)² + 8 = 0. Let's transform it into standard form:

1. Expand the square: (x-4)² = (x-4)(x-4) = x² - 8x + 16
2. Substitute back into the equation: x² - 8x + 16 + 8 = 0
3. Combine constant terms: x² - 8x + 24 = 0

Now the equation is in standard form: x² - 8x + 24 = 0

Solving the Equation

We can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Where:

• a = 1
• b = -8
• c = 24

Substituting the values into the formula:

x = (8 ± √((-8)² - 4 * 1 * 24)) / (2 * 1) x = (8 ± √(-32)) / 2 x = (8 ± 4√(-2)) / 2 x = 4 ± 2√(-2)

Since the square root of a negative number is imaginary, we can express the solution using the imaginary unit i, where i = √(-1):

x = 4 ± 2i√2

Therefore, the solutions to the quadratic equation (x-4)² + 8 = 0 are x = 4 + 2i√2 and x = 4 - 2i√2.