how to solve 11m2 + 14 = 47 using the square root (extracting the square)

To solve the equation \( 11m^2 + 14 = 47 \) by extracting the square root, follow these steps:

### Step 1: Isolate the \( m^2 \) term
Subtract 14 from both sides:
\[
11m^2 + 14 - 14 = 47 - 14
\]
\[
11m^2 = 33
\]

### Step 2: Divide by 11
Divide both sides of the equation by 11 to isolate \( m^2 \):
\[
m^2 = \frac{33}{11}
\]
\[
m^2 = 3
\]

### Step 3: Take the square root of both sides
To solve for \( m \), take the square root of both sides:
\[
m = \pm \sqrt{3}
\]

Thus, the solution is:
\[
m = \pm \sqrt{3}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How can I solve quadratic equations by factoring?
2. What are the steps to completing the square?
3. How do I solve quadratic equations using the quadratic formula?
4. What is the difference between rational and irrational solutions?
5. Can square roots be negative, and how do imaginary numbers relate to this?

**Tip:** Always check your solutions by plugging them back into the original equation.

how to solve 11m^2 + 14 = 47 using the square root (extracting the square)

Learn how to solve the equation 11m^2 + 14 = 47 using the square root method. This problem involves isolating the variable, dividing by the coefficient, and applying the square root property. Suitable for students in Grades 8-10.

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