Find all real solutions of the equation by first factoring the left hand side and then taking a square root:
x
2
+
10
x
+
25
=
4
 .

x
1
=
  
 and  
x
2
=
  
 with  
x
1
<
x
2
 

The given equation is:

\[
x^2 + 10x + 25 = 4
\]

### Step 1: Move the constant term to the other side

First, subtract 4 from both sides to set the equation equal to 0:

\[
x^2 + 10x + 25 - 4 = 0
\]

Simplifying:

\[
x^2 + 10x + 21 = 0
\]

### Step 2: Factor the quadratic expression

Now, we need to factor the left-hand side of the equation. We look for two numbers that multiply to give 21 and add to give 10. These numbers are 3 and 7, so we can factor the equation as:

\[
(x + 3)(x + 7) = 0
\]

### Step 3: Solve for \(x\)

Set each factor equal to zero:

\[
x + 3 = 0 \quad \text{or} \quad x + 7 = 0
\]

Solving these equations gives:

\[
x_1 = -3 \quad \text{and} \quad x_2 = -7
\]

Since \(x_1 < x_2\), we have:

\[
x_1 = -7 \quad \text{and} \quad x_2 = -3
\]

Thus, the real solutions are \(x_1 = -7\) and \(x_2 = -3\).

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Would you like more details or have any questions?

Here are 5 related questions:
1. What are the methods to factor quadratic equations?
2. How do you complete the square for a quadratic equation?
3. Can every quadratic equation be factored using integers?
4. How do you check if a quadratic equation has real or complex solutions?
5. What are the steps for solving a quadratic equation using the quadratic formula?

**Tip:** Always check if factoring is possible before using the quadratic formula for faster solutions.

Find all real solutions of the equation by first factoring the left-hand side and then taking a square root: x^2 + 10x + 25 = 4. x1 = and x2 = with x1 < x2

Learn how to solve the quadratic equation x^2 + 10x + 25 = 4 by factoring and finding real solutions. This detailed solution demonstrates factoring techniques and the zero product property, suitable for students in Grades 9-11.

Math Problem Statement

Find all real solutions of the equation by first factoring the left hand side and then taking a square root: x 2 + 10 x + 25

x 1

and
x 2

Solution

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