Solve for x x^2+4.5x+5=0

$x^{2} + 4.5 x + 5 = 0$

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 $a = 1$ , $b = 4.5$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 4.5 \pm \sqrt{{4.5}^{2} - 4 \cdot (1 \cdot 5)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

Raise $4.5$ to the power of $2$ .

$x = \frac{- 4.5 \pm \sqrt{20.25 - 4 \cdot 1 \cdot 5}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 5$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 4.5 \pm \sqrt{20.25 - 4 \cdot 5}}{2 \cdot 1}$

Multiply $- 4$ by $5$ .

$x = \frac{- 4.5 \pm \sqrt{20.25 - 20}}{2 \cdot 1}$

Subtract $20$ from $20.25$ .

$x = \frac{- 4.5 \pm \sqrt{0.25}}{2 \cdot 1}$

Rewrite $0.25$ as ${0.5}^{2}$ .

$x = \frac{- 4.5 \pm \sqrt{{0.5}^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 4.5 \pm 0.5}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 4.5 \pm 0.5}{2}$

Simplify $\frac{- 4.5 \pm 0.5}{2}$ .

$x = \frac{- 9 \pm 1}{4}$

Step 4

The final answer is the combination of both solutions.

$x = - 2, - \frac{5}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 2, - \frac{5}{2}$

Decimal Form:

$x = - 2, - 2.5$

Mixed Number Form:

$x = - 2, - 2 \frac{1}{2}$