Solve x² + 7x = 7 and give your answer correct to two decimal places.

To solve the quadratic equation \( x^2 + 7x = 7 \), we will follow these steps:

1. **Rearrange the equation**: Move all terms to one side of the equation to set it equal to zero.

\( x^2 + 7x - 7 = 0 \)

2. **Use the quadratic formula**: The quadratic formula is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

For the equation \( ax^2 + bx + c = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = 7 \)
- \( c = -7 \)

3. **Substitute the values into the quadratic formula**:

\[
x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-7)}}{2(1)}
\]

Simplifying:

\[
x = \frac{-7 \pm \sqrt{49 + 28}}{2}
\]

\[
x = \frac{-7 \pm \sqrt{77}}{2}
\]

4. **Calculate the square root**:

\[
\sqrt{77} \approx 8.77496
\]

5. **Find the two possible values for \( x \)**:

\[
x = \frac{-7 + 8.77496}{2} \quad \text{or} \quad x = \frac{-7 - 8.77496}{2}
\]

First, solving for the positive square root:

\[
x = \frac{-7 + 8.77496}{2} = \frac{1.77496}{2} \approx 0.89
\]

Now, solving for the negative square root:

\[
x = \frac{-7 - 8.77496}{2} = \frac{-15.77496}{2} \approx -7.89
\]

Thus, the two solutions to the equation are approximately:

\( x = 0.89 \) and \( x = -7.89 \) (correct to two decimal places).