Solve the quadratic equation using the Square Root Property.

left parenthesis 6 x plus 3 right parenthesis squared minus 6 equals negative 5

To solve the quadratic equation \((6x + 3)^2 - 6 = -5\) using the Square Root Property, follow these steps:

### Step 1: Isolate the squared term
We begin by isolating the squared term \((6x + 3)^2\).

\[
(6x + 3)^2 - 6 = -5
\]

Add 6 to both sides:

\[
(6x + 3)^2 = -5 + 6
\]

\[
(6x + 3)^2 = 1
\]

### Step 2: Apply the Square Root Property
Now, apply the Square Root Property. Taking the square root of both sides of the equation gives:

\[
6x + 3 = \pm \sqrt{1}
\]

Since \(\sqrt{1} = 1\), we have:

\[
6x + 3 = \pm 1
\]

### Step 3: Solve for \(x\)
Now, we'll solve for \(x\) in both cases.

#### Case 1: \(6x + 3 = 1\)
Subtract 3 from both sides:

\[
6x = 1 - 3
\]

\[
6x = -2
\]

Divide by 6:

\[
x = \frac{-2}{6} = \frac{-1}{3}
\]

#### Case 2: \(6x + 3 = -1\)
Subtract 3 from both sides:

\[
6x = -1 - 3
\]

\[
6x = -4
\]

Divide by 6:

\[
x = \frac{-4}{6} = \frac{-2}{3}
\]

### Final Answer:
The solutions to the equation are:

\[
x = \frac{-1}{3} \quad \text{or} \quad x = \frac{-2}{3}
\]

Would you like a detailed explanation of any step or further clarification?

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Here are 5 related questions for practice:

1. Solve \((2x + 5)^2 - 4 = 12\) using the Square Root Property.
2. Use the Square Root Property to solve \(4(x - 2)^2 = 64\).
3. Solve \(9x^2 = 81\) by applying the Square Root Property.
4. How would you solve \((3x + 1)^2 = 49\) using the Square Root Property?
5. Apply the Square Root Property to solve \((5x - 3)^2 = 25\).

**Tip**: Always remember to isolate the squared term first before applying the Square Root Property.

Solve the quadratic equation using the Square Root Property. (6x + 3)^2 - 6 = -5

Learn how to solve the quadratic equation (6x + 3)^2 - 6 = -5 using the Square Root Property. This step-by-step solution covers key algebra concepts, including isolating the squared term and solving for x. Suitable for students in Grades 9-11.

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