Pre-Algebra Examples

$- x^{2} - 4 x - 4 x = 3$

Step 1

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

$- x^{2} - 8 x = 3$

Step 2

Subtract $3$ from both sides of the equation.

$- x^{2} - 8 x - 3 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = - 1$ , $b = - 8$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (- 1 \cdot - 3)}}{2 \cdot - 1}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 1 \cdot - 3}}{2 \cdot - 1}$

Step 5.1.2

Multiply $- 4 \cdot - 1 \cdot - 3$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{8 \pm \sqrt{64 + 4 \cdot - 3}}{2 \cdot - 1}$

Step 5.1.2.2

Multiply $4$ by $- 3$ .

$x = \frac{8 \pm \sqrt{64 - 12}}{2 \cdot - 1}$

Step 5.1.3

Subtract $12$ from $64$ .

$x = \frac{8 \pm \sqrt{52}}{2 \cdot - 1}$

Step 5.1.4

Rewrite $52$ as $2^{2} \cdot 13$ .

Tap for more steps...

Step 5.1.4.1

Factor $4$ out of $52$ .

$x = \frac{8 \pm \sqrt{4 (13)}}{2 \cdot - 1}$

Step 5.1.4.2

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot - 1}$

Step 5.1.5

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{13}}{2 \cdot - 1}$

Step 5.2

Multiply $2$ by $- 1$ .

$x = \frac{8 \pm 2 \sqrt{13}}{- 2}$

Step 5.3

Simplify $\frac{8 \pm 2 \sqrt{13}}{- 2}$ .

$x = \frac{4 \pm \sqrt{13}}{- 1}$

Step 5.4

Move the negative one from the denominator of $\frac{4 \pm \sqrt{13}}{- 1}$ .

$x = - 1 \cdot (4 \pm \sqrt{13})$

Step 5.5

Rewrite $- 1 \cdot (4 \pm \sqrt{13})$ as $- (4 \pm \sqrt{13})$ .

$x = - (4 \pm \sqrt{13})$

Step 6

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 1 \cdot - 3}}{2 \cdot - 1}$

Step 6.1.2

Multiply $- 4 \cdot - 1 \cdot - 3$ .

Tap for more steps...

Step 6.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{8 \pm \sqrt{64 + 4 \cdot - 3}}{2 \cdot - 1}$

Step 6.1.2.2

Multiply $4$ by $- 3$ .

$x = \frac{8 \pm \sqrt{64 - 12}}{2 \cdot - 1}$

Step 6.1.3

Subtract $12$ from $64$ .

$x = \frac{8 \pm \sqrt{52}}{2 \cdot - 1}$

Step 6.1.4

Rewrite $52$ as $2^{2} \cdot 13$ .

Tap for more steps...

Step 6.1.4.1

Factor $4$ out of $52$ .

$x = \frac{8 \pm \sqrt{4 (13)}}{2 \cdot - 1}$

Step 6.1.4.2

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot - 1}$

Step 6.1.5

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{13}}{2 \cdot - 1}$

Step 6.2

Multiply $2$ by $- 1$ .

$x = \frac{8 \pm 2 \sqrt{13}}{- 2}$

Step 6.3

Simplify $\frac{8 \pm 2 \sqrt{13}}{- 2}$ .

$x = \frac{4 \pm \sqrt{13}}{- 1}$

Step 6.4

Move the negative one from the denominator of $\frac{4 \pm \sqrt{13}}{- 1}$ .

$x = - 1 \cdot (4 \pm \sqrt{13})$

Step 6.5

Rewrite $- 1 \cdot (4 \pm \sqrt{13})$ as $- (4 \pm \sqrt{13})$ .

$x = - (4 \pm \sqrt{13})$

Step 6.6

Change the $\pm$ to $+$ .

$x = - (4 + \sqrt{13})$

Step 6.7

Apply the distributive property.

$x = - 1 \cdot 4 - \sqrt{13}$

Step 6.8

Multiply $- 1$ by $4$ .

$x = - 4 - \sqrt{13}$

Step 7

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 7.1

Simplify the numerator.

Tap for more steps...

Step 7.1.1

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 1 \cdot - 3}}{2 \cdot - 1}$

Step 7.1.2

Multiply $- 4 \cdot - 1 \cdot - 3$ .

Tap for more steps...

Step 7.1.2.1

Multiply $- 4$ by $- 1$ .

$x = \frac{8 \pm \sqrt{64 + 4 \cdot - 3}}{2 \cdot - 1}$

Step 7.1.2.2

Multiply $4$ by $- 3$ .

$x = \frac{8 \pm \sqrt{64 - 12}}{2 \cdot - 1}$

Step 7.1.3

Subtract $12$ from $64$ .

$x = \frac{8 \pm \sqrt{52}}{2 \cdot - 1}$

Step 7.1.4

Rewrite $52$ as $2^{2} \cdot 13$ .

Tap for more steps...

Step 7.1.4.1

Factor $4$ out of $52$ .

$x = \frac{8 \pm \sqrt{4 (13)}}{2 \cdot - 1}$

Step 7.1.4.2

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 13}}{2 \cdot - 1}$

Step 7.1.5

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{13}}{2 \cdot - 1}$

Step 7.2

Multiply $2$ by $- 1$ .

$x = \frac{8 \pm 2 \sqrt{13}}{- 2}$

Step 7.3

Simplify $\frac{8 \pm 2 \sqrt{13}}{- 2}$ .

$x = \frac{4 \pm \sqrt{13}}{- 1}$

Step 7.4

Move the negative one from the denominator of $\frac{4 \pm \sqrt{13}}{- 1}$ .

$x = - 1 \cdot (4 \pm \sqrt{13})$

Step 7.5

Rewrite $- 1 \cdot (4 \pm \sqrt{13})$ as $- (4 \pm \sqrt{13})$ .

$x = - (4 \pm \sqrt{13})$

Step 7.6

Change the $\pm$ to $-$ .

$x = - (4 - \sqrt{13})$

Step 7.7

Apply the distributive property.

$x = - 1 \cdot 4 + \sqrt{13}$

Step 7.8

Multiply $- 1$ by $4$ .

$x = - 4 + \sqrt{13}$

Step 7.9

Multiply $- - \sqrt{13}$ .

Tap for more steps...

Step 7.9.1

Multiply $- 1$ by $- 1$ .

$x = - 4 + 1 \sqrt{13}$

Step 7.9.2

Multiply $\sqrt{13}$ by $1$ .

$x = - 4 + \sqrt{13}$

Step 8

The final answer is the combination of both solutions.

$x = - 4 - \sqrt{13}, - 4 + \sqrt{13}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = - 4 - \sqrt{13}, - 4 + \sqrt{13}$

Decimal Form:

$x = - 7.60555127 \dots, - 0.39444872 \dots$