(x+3)²=8

To solve the equation (x + 3)² = 8, we can follow these steps:

1. Expand the square: (x + 3)² = (x + 3)(x + 3) = x² + 6x + 9.

2. Set the expanded equation equal to 8: x² + 6x + 9 = 8.

3. Rearrange the equation, subtracting 8 from both sides: x² + 6x + 9 - 8 = 0.

4. Simplify the equation: x² + 6x + 1 = 0.

Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a).

In our case, the quadratic equation is x² + 6x + 1 = 0, which gives us: a = 1, b = 6, and c = 1.

Plugging these values into the quadratic formula, we have:

x = (-6 ± √(6² - 4(1)(1))) / (2(1)). x = (-6 ± √(36 - 4)) / 2. x = (-6 ± √(32)) / 2. x = (-6 ± 4√2) / 2.

Simplifying further:

x = -3 ± 2√2.

Therefore, the solutions to the equation (x + 3)² = 8 are:

x = -3 + 2√2, and x = -3 - 2√2.