To solve the equation [tex]\(4x^2 - 1 = 0\)[/tex], we'll follow these steps:
1. Set the equation to zero:
[tex]\[ 4x^2 - 1 = 0 \][/tex]
2. Add 1 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 4x^2 - 1 + 1 = 0 + 1 \][/tex]
[tex]\[ 4x^2 = 1 \][/tex]
3. Divide both sides by 4 to get [tex]\(x^2\)[/tex] alone:
[tex]\[ \frac{4x^2}{4} = \frac{1}{4} \][/tex]
[tex]\[ x^2 = \frac{1}{4} \][/tex]
4. Take the square root of both sides to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \pm \sqrt{\frac{1}{4}} \][/tex]
5. Simplify the square root:
[tex]\[ x = \pm \frac{1}{2} \][/tex]
Thus, the solutions to the equation [tex]\(4x^2 - 1 = 0\)[/tex] are:
[tex]\[ x = -\frac{1}{2} \][/tex]
and
[tex]\[ x = \frac{1}{2} \][/tex]
