Solve Using the Quadratic Formula x^2=-5x-3

$x^{2} = - 5 x - 3$

Step 1

Move all the expressions to the left side of the equation.

Add $5 x$ to both sides of the equation.

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

Add $3$ to both sides of the equation.

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

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 $a = 1$ , $b = 5$ , 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 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $3$ .

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

Subtract $12$ from $25$ .

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

Multiply $2$ by $1$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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