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].
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].
