Algebra Examples

$0 = {(5 x + 3)}^{2} + 2 x$

Step 1

Rewrite the equation as ${(5 x + 3)}^{2} + 2 x = 0$ .

${(5 x + 3)}^{2} + 2 x = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 25$ , $b = 32$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 32 \pm \sqrt{32^{2} - 4 \cdot (25 \cdot 9)}}{2 \cdot 25}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $32$ to the power of $2$ .

$x = \frac{- 32 \pm \sqrt{1024 - 4 \cdot 25 \cdot 9}}{2 \cdot 25}$

Step 4.1.2

Multiply $- 4 \cdot 25 \cdot 9$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $25$ .

$x = \frac{- 32 \pm \sqrt{1024 - 100 \cdot 9}}{2 \cdot 25}$

Step 4.1.2.2

Multiply $- 100$ by $9$ .

$x = \frac{- 32 \pm \sqrt{1024 - 900}}{2 \cdot 25}$

Step 4.1.3

Subtract $900$ from $1024$ .

$x = \frac{- 32 \pm \sqrt{124}}{2 \cdot 25}$

Step 4.1.4

Rewrite $124$ as $2^{2} \cdot 31$ .

Tap for more steps...

Step 4.1.4.1

Factor $4$ out of $124$ .

$x = \frac{- 32 \pm \sqrt{4 (31)}}{2 \cdot 25}$

Step 4.1.4.2

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

$x = \frac{- 32 \pm \sqrt{2^{2} \cdot 31}}{2 \cdot 25}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{- 32 \pm 2 \sqrt{31}}{2 \cdot 25}$

Step 4.2

Multiply $2$ by $25$ .

$x = \frac{- 32 \pm 2 \sqrt{31}}{50}$

Step 4.3

Simplify $\frac{- 32 \pm 2 \sqrt{31}}{50}$ .

$x = \frac{- 16 \pm \sqrt{31}}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 16 \pm \sqrt{31}}{25}$

Decimal Form:

$x = - 0.41728942 \dots, - 0.86271057 \dots$

Step 6