Algebra Examples

$x^{2} + 10 x + 13 = 0$

Step 1

Subtract $13$ from both sides of the equation.

$x^{2} + 10 x = - 13$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(5)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} + 10 x + {(5)}^{2} = - 13 + {(5)}^{2}$

Step 4

Simplify the equation.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Raise $5$ to the power of $2$ .

$x^{2} + 10 x + 25 = - 13 + {(5)}^{2}$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $- 13 + {(5)}^{2}$ .

Tap for more steps...

Step 4.2.1.1

Raise $5$ to the power of $2$ .

$x^{2} + 10 x + 25 = - 13 + 25$

Step 4.2.1.2

Add $- 13$ and $25$ .

$x^{2} + 10 x + 25 = 12$

Step 5

Factor the perfect trinomial square into ${(x + 5)}^{2}$ .

${(x + 5)}^{2} = 12$

Step 6

Solve the equation for $x$ .

Tap for more steps...

Step 6.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 5 = \pm \sqrt{12}$

Step 6.2

Simplify $\pm \sqrt{12}$ .

Tap for more steps...

Step 6.2.1

Rewrite $12$ as $2^{2} \cdot 3$ .

Tap for more steps...

Step 6.2.1.1

Factor $4$ out of $12$ .

$x + 5 = \pm \sqrt{4 (3)}$

Step 6.2.1.2

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

$x + 5 = \pm \sqrt{2^{2} \cdot 3}$

Step 6.2.2

Pull terms out from under the radical.

$x + 5 = \pm 2 \sqrt{3}$

Step 6.3

Subtract $5$ from both sides of the equation.

$x = \pm 2 \sqrt{3} - 5$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{3} - 5$

Decimal Form:

$x = - 1.53589838 \dots, - 8.46410161 \dots$