To solve the quadratic equation [tex]\(4 x^2 - 144 = 0\)[/tex], we can follow these steps:
1. Rewrite the Equation:
The given equation is:
[tex]\[
4 x^2 - 144 = 0
\][/tex]
2. Isolate the Quadratic Term:
Add 144 to both sides of the equation to isolate the quadratic term:
[tex]\[
4 x^2 - 144 + 144 = 0 + 144
\][/tex]
This simplifies to:
[tex]\[
4 x^2 = 144
\][/tex]
3. Solve for [tex]\(x^2\)[/tex]:
Divide both sides of the equation by 4 to solve for [tex]\(x^2\)[/tex]:
[tex]\[
\frac{4 x^2}{4} = \frac{144}{4}
\][/tex]
Simplifying this, we get:
[tex]\[
x^2 = 36
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To find the value of [tex]\(x\)[/tex], take the square root of both sides:
[tex]\[
x = \pm \sqrt{36}
\][/tex]
Since the square root of 36 is 6, we get:
[tex]\[
x = \pm 6
\][/tex]
5. Write the Solution:
There are two solutions for this equation:
[tex]\[
x = -6 \quad \text{and} \quad x = 6
\][/tex]
Thus, the solutions to the quadratic equation [tex]\( 4 x^2 - 144 = 0 \)[/tex] are [tex]\(x = -6\)[/tex] and [tex]\(x = 6\)[/tex].
