Basic Math Examples

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

Step 1

Subtract $4 y$ from both sides of the equation.

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

Step 2

Factor using the perfect square rule.

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Step 2.1

Rearrange terms.

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

Step 2.2

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

${(2 y)}^{2} - 4 y + 1 = 0$

Step 2.3

Rewrite $1$ as $1^{2}$ .

${(2 y)}^{2} - 4 y + 1^{2} = 0$

Step 2.4

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 y = 2 \cdot (2 y) \cdot 1$

Step 2.5

Rewrite the polynomial.

${(2 y)}^{2} - 2 \cdot (2 y) \cdot 1 + 1^{2} = 0$

Step 2.6

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 2 y$ and $b = 1$ .

${(2 y - 1)}^{2} = 0$

Step 3

Set the $2 y - 1$ equal to $0$ .

$2 y - 1 = 0$

Step 4

Solve for $y$ .

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Step 4.1

Add $1$ to both sides of the equation.

$2 y = 1$

Step 4.2

Divide each term in $2 y = 1$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 y = 1$ by $2$ .

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $y$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.5$