# What are the exact solutions of x^2 − 3x − 7 = 0?

Nov 13, 2016

4.54 and -1.54

#### Explanation:

${x}^{2} - 3 x - 7 = 0$

Here

$a = + 1$

$b = - 3$

$c = - 7$

$x = \frac{- \left(- 3\right) \pm \sqrt{{\left(- 3\right)}^{2} - 4 \times \left(1\right) \times \left(- 7\right)}}{2 \times \left(- 1\right)}$

After solving we get

$x = \frac{3 + \sqrt{37}}{2}$ and $x = \frac{3 - \sqrt{37}}{2}$

Therefore $x = 4.54 \mathmr{and} x = - 1.54$