Pre-Algebra Examples

$0.25 z^{2} = 0.6 z - 0.36$

Step 1

Subtract $0.6 z$ from both sides of the equation.

$0.25 z^{2} - 0.6 z = - 0.36$

Step 2

Add $0.36$ to both sides of the equation.

$0.25 z^{2} - 0.6 z + 0.36 = 0$

Step 3

Factor the left side of the equation.

Tap for more steps...

Step 3.1

Factor $0.01$ out of $0.25 z^{2} - 0.6 z + 0.36$ .

Tap for more steps...

Step 3.1.1

Factor $0.01$ out of $0.25 z^{2}$ .

$0.01 (25 z^{2}) - 0.6 z + 0.36 = 0$

Step 3.1.2

Factor $0.01$ out of $- 0.6 z$ .

$0.01 (25 z^{2}) + 0.01 (- 60 z) + 0.36 = 0$

Step 3.1.3

Factor $0.01$ out of $0.36$ .

$0.01 (25 z^{2}) + 0.01 (- 60 z) + 0.01 (36) = 0$

Step 3.1.4

Factor $0.01$ out of $0.01 (25 z^{2}) + 0.01 (- 60 z)$ .

$0.01 (25 z^{2} - 60 z) + 0.01 (36) = 0$

Step 3.1.5

Factor $0.01$ out of $0.01 (25 z^{2} - 60 z) + 0.01 (36)$ .

$0.01 (25 z^{2} - 60 z + 36) = 0$

Step 3.2

Factor using the perfect square rule.

Tap for more steps...

Step 3.2.1

Rewrite $25 z^{2}$ as ${(5 z)}^{2}$ .

$0.01 ({(5 z)}^{2} - 60 z + 36) = 0$

Step 3.2.2

Rewrite $36$ as $6^{2}$ .

$0.01 ({(5 z)}^{2} - 60 z + 6^{2}) = 0$

Step 3.2.3

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

$60 z = 2 \cdot (5 z) \cdot 6$

Step 3.2.4

Rewrite the polynomial.

$0.01 ({(5 z)}^{2} - 2 \cdot (5 z) \cdot 6 + 6^{2}) = 0$

Step 3.2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 5 z$ and $b = 6$ .

$0.01 {(5 z - 6)}^{2} = 0$

Step 4

Divide each term in $0.01 {(5 z - 6)}^{2} = 0$ by $0.01$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $0.01 {(5 z - 6)}^{2} = 0$ by $0.01$ .

$\frac{0.01 {(5 z - 6)}^{2}}{0.01} = \frac{0}{0.01}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $0.01$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{0.01 {(5 z - 6)}^{2}}{0.01} = \frac{0}{0.01}$

Step 4.2.1.2

Divide ${(5 z - 6)}^{2}$ by $1$ .

${(5 z - 6)}^{2} = \frac{0}{0.01}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $0.01$ .

${(5 z - 6)}^{2} = 0$

Step 5

Set the $5 z - 6$ equal to $0$ .

$5 z - 6 = 0$

Step 6

Solve for $z$ .

Tap for more steps...

Step 6.1

Add $6$ to both sides of the equation.

$5 z = 6$

Step 6.2

Divide each term in $5 z = 6$ by $5$ and simplify.

Tap for more steps...

Step 6.2.1

Divide each term in $5 z = 6$ by $5$ .

$\frac{5 z}{5} = \frac{6}{5}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

$\frac{5 z}{5} = \frac{6}{5}$

Step 6.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{6}{5}$