## Solving the Equation (x+4)^2 = 16x

This article will guide you through the process of solving the equation **(x+4)^2 = 16x**. We will use algebraic techniques to find the solutions for *x*.

### 1. Expanding the Equation

First, we need to expand the left side of the equation by using the FOIL (First, Outer, Inner, Last) method:

(x+4)^2 = (x+4)(x+4) = x^2 + 4x + 4x + 16 = x^2 + 8x + 16

Now our equation becomes:

**x^2 + 8x + 16 = 16x**

### 2. Rearranging the Equation

To solve for *x*, we need to rearrange the equation to have all terms on one side:

x^2 + 8x + 16 - 16x = 0

This simplifies to:

**x^2 - 8x + 16 = 0**

### 3. Solving the Quadratic Equation

The equation we have now is a quadratic equation. There are two main ways to solve quadratic equations:

**Factoring:**In this case, the equation can be factored easily: (x - 4)(x - 4) = 0 This gives us the solution**x = 4**. Since the factor (x - 4) is repeated, we have a double root, meaning the solution x = 4 appears twice.**Quadratic Formula:**The quadratic formula can be used to solve any quadratic equation in the form ax^2 + bx + c = 0. The formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 1, b = -8, and c = 16. Plugging these values into the formula gives:

x = (8 ± √((-8)^2 - 4 * 1 * 16)) / (2 * 1) x = (8 ± √(0)) / 2 x = 4

### Conclusion

The solution to the equation (x+4)^2 = 16x is **x = 4**. We found this solution using both factoring and the quadratic formula, confirming the solution.