Solve for y 1-4y^2=0

$1 - 4 y^{2} = 0$

Step 1

Subtract $1$ from both sides of the equation.

$- 4 y^{2} = - 1$

Step 2

Divide each term in $- 4 y^{2} = - 1$ by $- 4$ and simplify.

Divide each term in $- 4 y^{2} = - 1$ by $- 4$ .

$\frac{- 4 y^{2}}{- 4} = \frac{- 1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y^{2}}{- 4} = \frac{- 1}{- 4}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{- 1}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y^{2} = \frac{1}{4}$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{\frac{1}{4}}$

Step 4

Simplify $\pm \sqrt{\frac{1}{4}}$ .

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$y = \pm \frac{\sqrt{1}}{\sqrt{4}}$

Any root of $1$ is $1$ .

$y = \pm \frac{1}{\sqrt{4}}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$y = \pm \frac{1}{\sqrt{2^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm \frac{1}{2}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{1}{2}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{1}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{1}{2}, - \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{2}, - \frac{1}{2}$

Decimal Form:

$y = 0.5, - 0.5$