Basic Math Examples

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

Step 1

Subtract $1$ from both sides of the equation.

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

Step 2

Factor the left side of the equation.

Tap for more steps...

Step 2.1

Factor $- 1$ out of $4 s - 4 s^{2} - 1$ .

Tap for more steps...

Step 2.1.1

Reorder $4 s$ and $- 4 s^{2}$ .

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

Step 2.1.2

Factor $- 1$ out of $- 4 s^{2}$ .

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

Step 2.1.3

Factor $- 1$ out of $4 s$ .

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

Step 2.1.4

Rewrite $- 1$ as $- 1 (1)$ .

$- (4 s^{2}) - (- 4 s) - 1 \cdot 1 = 0$

Step 2.1.5

Factor $- 1$ out of $- (4 s^{2}) - (- 4 s)$ .

$- (4 s^{2} - 4 s) - 1 \cdot 1 = 0$

Step 2.1.6

Factor $- 1$ out of $- (4 s^{2} - 4 s) - 1 (1)$ .

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

Step 2.2

Factor using the perfect square rule.

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Rewrite the polynomial.

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

Step 2.2.5

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

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

Step 3

Divide each term in $- {(2 s - 1)}^{2} = 0$ by $- 1$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- {(2 s - 1)}^{2} = 0$ by $- 1$ .

$\frac{- {(2 s - 1)}^{2}}{- 1} = \frac{0}{- 1}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{{(2 s - 1)}^{2}}{1} = \frac{0}{- 1}$

Step 3.2.2

Divide ${(2 s - 1)}^{2}$ by $1$ .

${(2 s - 1)}^{2} = \frac{0}{- 1}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $0$ by $- 1$ .

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

Step 4

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

$2 s - 1 = 0$

Step 5

Solve for $s$ .

Tap for more steps...

Step 5.1

Add $1$ to both sides of the equation.

$2 s = 1$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

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

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

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

Step 5.2.2.1.2

Divide $s$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$s = 0.5$