Finite Math Examples

$x = 2 {(x - 4)}^{2} - 7$

Step 1

Simplify $2 {(x - 4)}^{2} - 7$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

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

$x = 2 ((x - 4) (x - 4)) - 7$

Step 1.1.2

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

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$x = 2 (x (x - 4) - 4 (x - 4)) - 7$

Step 1.1.2.2

Apply the distributive property.

$x = 2 (x \cdot x + x \cdot - 4 - 4 (x - 4)) - 7$

Step 1.1.2.3

Apply the distributive property.

$x = 2 (x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4) - 7$

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

Multiply $x$ by $x$ .

$x = 2 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4) - 7$

Step 1.1.3.1.2

Move $- 4$ to the left of $x$ .

$x = 2 (x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4) - 7$

Step 1.1.3.1.3

Multiply $- 4$ by $- 4$ .

$x = 2 (x^{2} - 4 x - 4 x + 16) - 7$

Step 1.1.3.2

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

$x = 2 (x^{2} - 8 x + 16) - 7$

Step 1.1.4

Apply the distributive property.

$x = 2 x^{2} + 2 (- 8 x) + 2 \cdot 16 - 7$

Step 1.1.5

Simplify.

Tap for more steps...

Step 1.1.5.1

Multiply $- 8$ by $2$ .

$x = 2 x^{2} - 16 x + 2 \cdot 16 - 7$

Step 1.1.5.2

Multiply $2$ by $16$ .

$x = 2 x^{2} - 16 x + 32 - 7$

Step 1.2

Subtract $7$ from $32$ .

$x = 2 x^{2} - 16 x + 25$

Step 2

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

$x \approx 1.89150471, 6.60849528$

Step 3