Basic Math Examples

$3 a^{2} + 6 a - 45 = 3$

Step 1

Subtract $3$ from both sides of the equation.

$3 a^{2} + 6 a - 45 - 3 = 0$

Step 2

Subtract $3$ from $- 45$ .

$3 a^{2} + 6 a - 48 = 0$

Step 3

Factor $3$ out of $3 a^{2} + 6 a - 48$ .

Tap for more steps...

Step 3.1

Factor $3$ out of $3 a^{2}$ .

$3 (a^{2}) + 6 a - 48 = 0$

Step 3.2

Factor $3$ out of $6 a$ .

$3 (a^{2}) + 3 (2 a) - 48 = 0$

Step 3.3

Factor $3$ out of $- 48$ .

$3 a^{2} + 3 (2 a) + 3 \cdot - 16 = 0$

Step 3.4

Factor $3$ out of $3 a^{2} + 3 (2 a)$ .

$3 (a^{2} + 2 a) + 3 \cdot - 16 = 0$

Step 3.5

Factor $3$ out of $3 (a^{2} + 2 a) + 3 \cdot - 16$ .

$3 (a^{2} + 2 a - 16) = 0$

Step 4

Divide each term in $3 (a^{2} + 2 a - 16) = 0$ by $3$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 (a^{2} + 2 a - 16) = 0$ by $3$ .

$\frac{3 (a^{2} + 2 a - 16)}{3} = \frac{0}{3}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{3 (a^{2} + 2 a - 16)}{3} = \frac{0}{3}$

Step 4.2.1.2

Divide $a^{2} + 2 a - 16$ by $1$ .

$a^{2} + 2 a - 16 = \frac{0}{3}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $0$ by $3$ .

$a^{2} + 2 a - 16 = 0$

Step 5

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 6

Substitute the values $a = 1$ , $b = 2$ , and $c = - 16$ into the quadratic formula and solve for $a$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 16)}}{2 \cdot 1}$

Step 7

Simplify.

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

Raise $2$ to the power of $2$ .

$a = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 16}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4 \cdot 1 \cdot - 16$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $1$ .

$a = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 16}}{2 \cdot 1}$

Step 7.1.2.2

Multiply $- 4$ by $- 16$ .

$a = \frac{- 2 \pm \sqrt{4 + 64}}{2 \cdot 1}$

Step 7.1.3

Add $4$ and $64$ .

$a = \frac{- 2 \pm \sqrt{68}}{2 \cdot 1}$

Step 7.1.4

Rewrite $68$ as $2^{2} \cdot 17$ .

Tap for more steps...

Step 7.1.4.1

Factor $4$ out of $68$ .

$a = \frac{- 2 \pm \sqrt{4 (17)}}{2 \cdot 1}$

Step 7.1.4.2

Rewrite $4$ as $2^{2}$ .

$a = \frac{- 2 \pm \sqrt{2^{2} \cdot 17}}{2 \cdot 1}$

Step 7.1.5

Pull terms out from under the radical.

$a = \frac{- 2 \pm 2 \sqrt{17}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$a = \frac{- 2 \pm 2 \sqrt{17}}{2}$

Step 7.3

Simplify $\frac{- 2 \pm 2 \sqrt{17}}{2}$ .

$a = - 1 \pm \sqrt{17}$

Step 8

The final answer is the combination of both solutions.

$a = - 1 + \sqrt{17}, - 1 - \sqrt{17}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$a = - 1 + \sqrt{17}, - 1 - \sqrt{17}$

Decimal Form:

$a = 3.12310562 \dots, - 5.12310562 \dots$