Let's solve the equation [tex]\( 2x^2 - 3 = 15 \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[
2x^2 - 3 = 15
\][/tex]
2. Isolate the term with the variable:
Add 3 to both sides of the equation to move the constant term to the right side:
[tex]\[
2x^2 - 3 + 3 = 15 + 3
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x^2 = 18
\][/tex]
3. Solve for [tex]\( x^2 \)[/tex]:
Divide both sides of the equation by 2 to isolate [tex]\( x^2 \)[/tex]:
[tex]\[
\frac{2x^2}{2} = \frac{18}{2}
\][/tex]
Simplifying, we obtain:
[tex]\[
x^2 = 9
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To remove the square, take the square root of both sides of the equation. Remember that the square root can yield both positive and negative results:
[tex]\[
x = \pm \sqrt{9}
\][/tex]
5. Simplify the square root:
Since the square root of 9 is 3, we have:
[tex]\[
x = \pm 3
\][/tex]
Therefore, the solutions to the equation [tex]\( 2x^2 - 3 = 15 \)[/tex] are:
[tex]\[
x = 3 \quad \text{and} \quad x = -3
\][/tex]
