Solve the equation.
\[
36 x^{2}-1=0
\]

Answer

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Answer

The solutions to the equation are \(\boxed{-\frac{1}{6}}\) and \(\boxed{\frac{1}{6}}\).

Steps

Step 1 ：The given equation is \(36x^{2}-1=0\).

Step 2 ：This is a quadratic equation in the form of \(ax^{2} + bx + c = 0\).

Step 3 ：We can solve it by using the quadratic formula \(x = [-b ± sqrt(b^{2} - 4ac)] / 2a\).

Step 4 ：However, in this case, the equation is a special case of quadratic equation, which is a difference of squares.

Step 5 ：It can be factored into \((6x - 1)(6x + 1) = 0\).

Step 6 ：We can solve for x by setting each factor equal to zero.

Step 7 ：The solutions to the equation are \(\boxed{-\frac{1}{6}}\) and \(\boxed{\frac{1}{6}}\).