To solve the quadratic equation [tex]\(6 + 3x^2 = 18\)[/tex], follow these steps:
1. Isolate the quadratic term:
To start, we need to move all terms to one side so that we can set the equation to zero. First, subtract 18 from both sides of the equation:
[tex]\[
6 + 3x^2 - 18 = 0
\][/tex]
2. Simplify the equation:
Combine like terms on the left side:
[tex]\[
3x^2 - 12 = 0
\][/tex]
3. Factor out the common factor:
We notice that both terms on the left side can be divided by the common factor of 3:
[tex]\[
x^2 - 4 = 0
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
This equation is a difference of squares, which can be factored further:
[tex]\[
(x - 2)(x + 2) = 0
\][/tex]
Set each factor equal to zero:
[tex]\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\][/tex]
Solving these two equations gives us the solutions:
[tex]\[
x = 2 \quad \text{or} \quad x = -2
\][/tex]
Therefore, the solutions to the quadratic equation [tex]\(6 + 3x^2 = 18\)[/tex] are:
[tex]\[
x = 2 \quad \text{and} \quad x = -2
\][/tex]
