## Solving the Quadratic Equation: (x+2)^2 = 9(x^2-4x+4)

This article will guide you through the steps of solving the quadratic equation (x+2)^2 = 9(x^2-4x+4).

### Expanding and Simplifying

First, we need to expand both sides of the equation:

**Left side:**(x+2)^2 = (x+2)(x+2) = x^2 + 4x + 4**Right side:**9(x^2 - 4x + 4) = 9x^2 - 36x + 36

Now our equation becomes: x^2 + 4x + 4 = 9x^2 - 36x + 36

### Rearranging the Equation

To solve for x, we need to rearrange the equation into the standard quadratic form (ax^2 + bx + c = 0). Subtract x^2, 4x, and 4 from both sides:

0 = 8x^2 - 40x + 32

### Solving the Quadratic Equation

We now have a quadratic equation in standard form. We can solve this using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 8, b = -40, and c = 32.

Substituting the values into the quadratic formula:

x = (40 ± √((-40)^2 - 4 * 8 * 32)) / (2 * 8) x = (40 ± √(1600 - 1024)) / 16 x = (40 ± √576) / 16 x = (40 ± 24) / 16

This gives us two solutions:

**x1 = (40 + 24) / 16 = 64 / 16 = 4****x2 = (40 - 24) / 16 = 16 / 16 = 1**

### Conclusion

Therefore, the solutions to the quadratic equation (x+2)^2 = 9(x^2-4x+4) are **x = 4** and **x = 1**.