Basic Math Examples

$z^{2} + 4 = 4 z$

Step 1

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

$z^{2} + 4 - 4 z = 0$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rearrange terms.

$z^{2} - 4 z + 4 = 0$

Step 2.2

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

$z^{2} - 4 z + 2^{2} = 0$

Step 2.3

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

$4 z = 2 \cdot z \cdot 2$

Step 2.4

Rewrite the polynomial.

$z^{2} - 2 \cdot z \cdot 2 + 2^{2} = 0$

Step 2.5

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

${(z - 2)}^{2} = 0$

Step 3

Set the $z - 2$ equal to $0$ .

$z - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$z = 2$