Answer :
Sure! Let's solve the equation [tex]\(3x^2 = 27\)[/tex] step by step:
1. Divide Both Sides by 3:
Start by isolating [tex]\(x^2\)[/tex] on one side of the equation. You can do this by dividing both sides of the equation by 3:
[tex]\[
x^2 = \frac{27}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 9
\][/tex]
2. Take the Square Root of Both Sides:
To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that taking the square root of a number gives two solutions: a positive root and a negative root.
[tex]\[
x = \pm \sqrt{9}
\][/tex]
3. Calculate the Solutions:
- The positive square root of 9 is 3, so one solution is [tex]\(x = 3\)[/tex].
- The negative square root of 9 is -3, so the other solution is [tex]\(x = -3\)[/tex].
Therefore, the solutions for the equation [tex]\(3x^2 = 27\)[/tex] are [tex]\(x = 3\)[/tex] and [tex]\(x = -3\)[/tex].
1. Divide Both Sides by 3:
Start by isolating [tex]\(x^2\)[/tex] on one side of the equation. You can do this by dividing both sides of the equation by 3:
[tex]\[
x^2 = \frac{27}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 9
\][/tex]
2. Take the Square Root of Both Sides:
To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember that taking the square root of a number gives two solutions: a positive root and a negative root.
[tex]\[
x = \pm \sqrt{9}
\][/tex]
3. Calculate the Solutions:
- The positive square root of 9 is 3, so one solution is [tex]\(x = 3\)[/tex].
- The negative square root of 9 is -3, so the other solution is [tex]\(x = -3\)[/tex].
Therefore, the solutions for the equation [tex]\(3x^2 = 27\)[/tex] are [tex]\(x = 3\)[/tex] and [tex]\(x = -3\)[/tex].
