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how to solve using square root (extracting the square)

The equation in the image is:

\[
11m^2 + 19 = 47
\]

You want to solve for \( m \) using the square root method. Here's a step-by-step approach:

### Step 1: Isolate the quadratic term
Subtract 19 from both sides of the equation:

\[
11m^2 = 47 - 19
\]

Simplifying:

\[
11m^2 = 28
\]

### Step 2: Divide by the coefficient of \( m^2 \)
Now divide both sides by 11 to get \( m^2 \) alone:

\[
m^2 = \frac{28}{11}
\]

### Step 3: Take the square root of both sides
To solve for \( m \), take the square root of both sides of the equation:

\[
m = \pm \sqrt{\frac{28}{11}}
\]

This simplifies to:

\[
m = \pm \frac{\sqrt{28}}{\sqrt{11}}
\]

### Step 4: Simplify the square root
We can simplify \( \sqrt{28} \) as:

\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]

Thus, the solution becomes:

\[
m = \pm \frac{2\sqrt{7}}{\sqrt{11}}
\]

### Final Answer:
\[
m = \pm \frac{2\sqrt{7}}{\sqrt{11}}
\]

This is the solution in its exact form. If you want a decimal approximation:

\[
m \approx \pm 1.59
\]

Would you like more details or a further breakdown of any steps?

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Here are 5 related questions:
1. What is the general process of solving quadratic equations using square roots?
2. How can you simplify expressions involving square roots?
3. What is the difference between solving using square roots and factoring?
4. Can you apply the square root method to equations with complex solutions?
5. How do you solve quadratic equations where the discriminant is negative?

**Tip:** Always check whether the number under the square root can be simplified to make calculations easier.

How to solve the equation 11m^2 + 19 = 47 using the square root method?

Learn how to solve the quadratic equation 11m^2 + 19 = 47 using the square root method with a step-by-step solution. This guide covers key algebraic concepts and simplifies the process to find the exact and approximate solutions. Suitable for students in Grades 9-11.

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