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.