Algebra Examples

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

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 1$ , $b = 5$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (1 \cdot 3)}}{2 \cdot 1}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

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

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$

Step 3.1.2

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

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Step 3.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 3}}{2 \cdot 1}$

Step 3.1.2.2

Multiply $- 4$ by $3$ .

$x = \frac{- 5 \pm \sqrt{25 - 12}}{2 \cdot 1}$

Step 3.1.3

Subtract $12$ from $25$ .

$x = \frac{- 5 \pm \sqrt{13}}{2 \cdot 1}$

Step 3.2

Multiply $2$ by $1$ .

$x = \frac{- 5 \pm \sqrt{13}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{13}}{2}$

Decimal Form:

$x = - 0.69722436 \dots, - 4.30277563 \dots$