Solve the quadratic equation using the square root property.
​(13kplus1​)squaredminus3equals96

We are given the quadratic equation:

\[
(13k + 1)^2 - 3 = 96
\]

To solve this equation using the square root property, let's follow the steps:

### Step 1: Isolate the squared term
Start by moving \(-3\) to the other side of the equation:

\[
(13k + 1)^2 = 96 + 3
\]

\[
(13k + 1)^2 = 99
\]

### Step 2: Apply the square root property
Now take the square root of both sides:

\[
13k + 1 = \pm \sqrt{99}
\]

\[
13k + 1 = \pm \sqrt{9 \times 11}
\]

\[
13k + 1 = \pm 3\sqrt{11}
\]

### Step 3: Solve for \( k \)
Next, solve for \( k \) by first subtracting 1 from both sides:

\[
13k = -1 \pm 3\sqrt{11}
\]

Now, divide by 13:

\[
k = \frac{-1 \pm 3\sqrt{11}}{13}
\]

Thus, the solution for \( k \) is:

\[
k = \frac{-1 + 3\sqrt{11}}{13} \quad \text{or} \quad k = \frac{-1 - 3\sqrt{11}}{13}
\]

These are the two possible solutions for \( k \).

Would you like further details on any of these steps?

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Here are 5 related questions for further exploration:

1. How do you simplify square roots of non-perfect squares like \( \sqrt{99} \)?
2. What is the general form of a quadratic equation?
3. How does the square root property differ from factoring when solving quadratics?
4. What are other methods to solve quadratic equations besides the square root property?
5. How can the quadratic formula be used to solve any quadratic equation?

**Tip:** Always ensure that the squared term is isolated before applying the square root property.

Solve the quadratic equation using the square root property: (13k + 1)^2 - 3 = 96

Discover how to solve the quadratic equation (13k + 1)^2 - 3 = 96 using the square root property. This step-by-step guide covers algebraic concepts and theorems, making it perfect for students in Grades 9-11.

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