Finite Math Examples

$25 - {(4 x - 1)}^{2} = 0$

Step 1

Simplify $25 - {(4 x - 1)}^{2}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite ${(4 x - 1)}^{2}$ as $(4 x - 1) (4 x - 1)$ .

$25 - ((4 x - 1) (4 x - 1)) = 0$

Step 1.1.2

Expand $(4 x - 1) (4 x - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$25 - (4 x (4 x - 1) - 1 (4 x - 1)) = 0$

Step 1.1.2.2

Apply the distributive property.

$25 - (4 x (4 x) + 4 x \cdot - 1 - 1 (4 x - 1)) = 0$

Step 1.1.2.3

Apply the distributive property.

$25 - (4 x (4 x) + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Rewrite using the commutative property of multiplication.

$25 - (4 \cdot 4 x \cdot x + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.2.1

Move $x$ .

$25 - (4 \cdot 4 (x \cdot x) + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3.1.2.2

Multiply $x$ by $x$ .

$25 - (4 \cdot 4 x^{2} + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3.1.3

Multiply $4$ by $4$ .

$25 - (16 x^{2} + 4 x \cdot - 1 - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3.1.4

Multiply $- 1$ by $4$ .

$25 - (16 x^{2} - 4 x - 1 (4 x) - 1 \cdot - 1) = 0$

Step 1.1.3.1.5

Multiply $4$ by $- 1$ .

$25 - (16 x^{2} - 4 x - 4 x - 1 \cdot - 1) = 0$

Step 1.1.3.1.6

Multiply $- 1$ by $- 1$ .

$25 - (16 x^{2} - 4 x - 4 x + 1) = 0$

Step 1.1.3.2

Subtract $4 x$ from $- 4 x$ .

$25 - (16 x^{2} - 8 x + 1) = 0$

Step 1.1.4

Apply the distributive property.

$25 - (16 x^{2}) - (- 8 x) - 1 \cdot 1 = 0$

Step 1.1.5

Simplify.

Tap for more steps...

Step 1.1.5.1

Multiply $16$ by $- 1$ .

$25 - 16 x^{2} - (- 8 x) - 1 \cdot 1 = 0$

Step 1.1.5.2

Multiply $- 8$ by $- 1$ .

$25 - 16 x^{2} + 8 x - 1 \cdot 1 = 0$

Step 1.1.5.3

Multiply $- 1$ by $1$ .

$25 - 16 x^{2} + 8 x - 1 = 0$

Step 1.2

Subtract $1$ from $25$ .

$- 16 x^{2} + 8 x + 24 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 1, \frac{3}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - 1, \frac{3}{2}$

Decimal Form:

$x = - 1, 1.5$

Mixed Number Form:

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

Step 4