(x+3)^2-4=0

2 min read Jun 16, 2024

Solving the Quadratic Equation: (x+3)^2 - 4 = 0

This article will guide you through the process of solving the quadratic equation (x+3)^2 - 4 = 0. We will use various methods to find the solutions for 'x'.

1. Expanding and Simplifying

First, let's expand the equation:

(x+3)^2 - 4 = 0 x^2 + 6x + 9 - 4 = 0 x^2 + 6x + 5 = 0

Now we have a standard quadratic equation in the form ax^2 + bx + c = 0.

2. Factoring

We can solve this equation by factoring:

(x + 1)(x + 5) = 0

This gives us two possible solutions:

x + 1 = 0 => x = -1
x + 5 = 0 => x = -5

3. Quadratic Formula

The quadratic formula can be used to solve any quadratic equation:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation:

a = 1
b = 6
c = 5

Substituting these values into the quadratic formula:

x = (-6 ± √(6^2 - 4 * 1 * 5)) / (2 * 1) x = (-6 ± √16) / 2 x = (-6 ± 4) / 2

This gives us two solutions:

x = (-6 + 4) / 2 = -1
x = (-6 - 4) / 2 = -5

Conclusion

We have successfully solved the quadratic equation (x+3)^2 - 4 = 0 using two methods: factoring and the quadratic formula. Both methods give us the same solutions: x = -1 and x = -5.