To solve the equation \( x^2 + 10x + 25 = 7 \), let's follow these steps:

### Step 1: Simplify the equation
Move 7 to the left side to set the equation to 0:
\[
x^2 + 10x + 25 - 7 = 0
\]
\[
x^2 + 10x + 18 = 0
\]

### Step 2: Solve using the quadratic formula
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), the solution is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, \( a = 1 \), \( b = 10 \), and \( c = 18 \).

Let's plug these values into the quadratic formula:
\[
x = \frac{-10 \pm \sqrt{10^2 - 4(1)(18)}}{2(1)}
\]
\[
x = \frac{-10 \pm \sqrt{100 - 72}}{2}
\]
\[
x = \frac{-10 \pm \sqrt{28}}{2}
\]
\[
x = \frac{-10 \pm 2\sqrt{7}}{2}
\]
\[
x = -5 \pm \sqrt{7}
\]

### Final Solution:
The two solutions are:
\[
x = -5 + \sqrt{7} \quad \text{or} \quad x = -5 - \sqrt{7}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the discriminant affect the number of solutions in a quadratic equation?
2. Can you factor \( x^2 + 10x + 18 \) instead of using the quadratic formula?
3. What are the properties of the solutions in terms of their decimal values?
4. How do you complete the square to solve quadratic equations?
5. Can a quadratic equation have complex solutions?

**Tip:** The discriminant \( b^2 - 4ac \) helps determine the nature of the roots (real or complex).

Learn how to solve the quadratic equation x^2 + 10x + 25 = 7 using the quadratic formula. This step-by-step solution covers algebraic concepts, including solving for the roots using the discriminant and quadratic formula. Suitable for students in Grades 9-11.

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