High School

Solve [tex]$3x^2 - 1 = 47$[/tex] using the square root property.

A. [tex]$x = 2, -2$[/tex]

B. [tex]$x = 4, -4$[/tex]

C. [tex]$x = 16, -16$[/tex]

D. [tex]$x = 7, -7$[/tex]

Answer :

Sure! Let's solve the equation [tex]\(3x^2 - 1 = 47\)[/tex] using the square root property, step by step.

1. Start with the given equation:

[tex]\[
3x^2 - 1 = 47
\][/tex]

2. Isolate the [tex]\(x^2\)[/tex] term:

Add 1 to both sides of the equation to get:

[tex]\[
3x^2 = 48
\][/tex]

3. Solve for [tex]\(x^2\)[/tex]:

Divide both sides of the equation by 3 to isolate [tex]\(x^2\)[/tex]:

[tex]\[
x^2 = \frac{48}{3}
\][/tex]

Simplifying the right side gives:

[tex]\[
x^2 = 16
\][/tex]

4. Use the square root property:

To solve for [tex]\(x\)[/tex], take the square root of both sides. When using the square root property, remember to consider both the positive and negative roots:

[tex]\[
x = \sqrt{16} \quad \text{or} \quad x = -\sqrt{16}
\][/tex]

This gives:

[tex]\[
x = 4 \quad \text{or} \quad x = -4
\][/tex]

So, the solution to the equation [tex]\(3x^2 - 1 = 47\)[/tex] is [tex]\(x = 4\)[/tex] or [tex]\(x = -4\)[/tex].