## Solving the Quadratic Equation: (7x+2)^2 + 6(7x+2) = 27

This article will guide you through the steps of solving the quadratic equation (7x+2)^2 + 6(7x+2) = 27.

### 1. Simplifying the Equation

First, we need to simplify the equation by expanding the square and distributing the 6:

- (7x+2)^2 = (7x+2)(7x+2) = 49x^2 + 28x + 4
- 6(7x+2) = 42x + 12

Now, the equation becomes:

49x^2 + 28x + 4 + 42x + 12 = 27

### 2. Rearranging the Equation

Next, we need to move all the terms to one side of the equation to get a standard quadratic equation:

49x^2 + 70x + 16 - 27 = 0

Simplifying further:

49x^2 + 70x - 11 = 0

### 3. Solving the Quadratic Equation

We can now solve this quadratic equation using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where:

- a = 49
- b = 70
- c = -11

Substituting these values into the quadratic formula, we get:

x = (-70 ± √(70^2 - 4 * 49 * -11)) / (2 * 49)

Simplifying:

x = (-70 ± √(4900 + 2156)) / 98

x = (-70 ± √7056) / 98

x = (-70 ± 84) / 98

This gives us two solutions:

- x = (-70 + 84) / 98 = 14 / 98 = 1 / 7
- x = (-70 - 84) / 98 = -154 / 98 = -11 / 7

### 4. Conclusion

Therefore, the solutions to the quadratic equation (7x+2)^2 + 6(7x+2) = 27 are **x = 1/7** and **x = -11/7**.