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

A. [tex]x = 7, -7[/tex]

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

C. [tex]x = 2, -2[/tex]

D. [tex]x = 16, -16[/tex]

Answer :

To solve the equation [tex]\(3x^2 - 1 = 47\)[/tex] using the square root property, follow these steps:

1. Isolate the [tex]\(x^2\)[/tex] term:
Start by adding 1 to both sides of the equation to get rid of the constant on the left side:
[tex]\[
3x^2 - 1 + 1 = 47 + 1
\][/tex]
This simplifies to:
[tex]\[
3x^2 = 48
\][/tex]

2. Divide both sides by 3:
To isolate [tex]\(x^2\)[/tex], divide both sides of the equation by 3:
[tex]\[
x^2 = \frac{48}{3}
\][/tex]
Simplifying the right side gives:
[tex]\[
x^2 = 16
\][/tex]

3. Use the square root property:
Take the square root of both sides of the equation. Remember that taking the square root of both sides will result in two solutions, the positive and negative square roots:
[tex]\[
x = \sqrt{16} \quad \text{or} \quad x = -\sqrt{16}
\][/tex]
This gives us:
[tex]\[
x = 4 \quad \text{or} \quad x = -4
\][/tex]

Therefore, the solutions to the equation [tex]\(3x^2 - 1 = 47\)[/tex] are [tex]\(x = 4\)[/tex] and [tex]\(x = -4\)[/tex].

Thanks for taking the time to read Solve tex 3x 2 1 47 tex using the square root property A tex x 7 7 tex B tex x 4 4 tex C. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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