Finite Math Examples

$2 x (x + 3) = x^{2} + 3 x + 70$

Step 1

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $x^{2}$ from both sides of the equation.

$2 x (x + 3) - x^{2} = 3 x + 70$

Step 1.2

Subtract $3 x$ from both sides of the equation.

$2 x (x + 3) - x^{2} - 3 x = 70$

Step 1.3

Subtract $70$ from both sides of the equation.

$2 x (x + 3) - x^{2} - 3 x - 70 = 0$

Step 2

Simplify $2 x (x + 3) - x^{2} - 3 x - 70$ .

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot 3 - x^{2} - 3 x - 70 = 0$

Step 2.1.2

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

Tap for more steps...

Step 2.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot 3 - x^{2} - 3 x - 70 = 0$

Step 2.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot 3 - x^{2} - 3 x - 70 = 0$

Step 2.1.3

Multiply $3$ by $2$ .

$2 x^{2} + 6 x - x^{2} - 3 x - 70 = 0$

Step 2.2

Subtract $x^{2}$ from $2 x^{2}$ .

$x^{2} + 6 x - 3 x - 70 = 0$

Step 2.3

Subtract $3 x$ from $6 x$ .

$x^{2} + 3 x - 70 = 0$

Step 3

Factor $x^{2} + 3 x - 70$ using the AC method.

Tap for more steps...

Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 70$ and whose sum is $3$ .

$- 7, 10$

Step 3.2

Write the factored form using these integers.

$(x - 7) (x + 10) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 7 = 0$

$x + 10 = 0$

Step 5

Set $x - 7$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Step 5.2

Add $7$ to both sides of the equation.

$x = 7$

Step 6

Set $x + 10$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 6.1

Set $x + 10$ equal to $0$ .

$x + 10 = 0$

Step 6.2

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 7

The final solution is all the values that make $(x - 7) (x + 10) = 0$ true.

$x = 7, - 10$