How do you solve 2x^2 - 10x + 7 = 0 using the quadratic formula?

Mar 20, 2018

$x = \frac{5 + \sqrt{11}}{2}$ or $x = \frac{5 - \sqrt{11}}{2}$

Explanation:

Quadratic formula gives the solution of a quadratic equation. For a quaddratic equation $a {x}^{2} + b x + c = 0$, the roots given by quadratic formula are $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$.

Hence for $2 {x}^{2} - 10 x + 7 = 0$, we have $a = 2$, $b = - 10$ and $c = 7$ and hence solution is

$\frac{- \left(- 10\right) \pm \sqrt{{\left(- 10\right)}^{2} - 4 \cdot 2 \cdot 7}}{2 \cdot 2}$

= $\frac{10 \pm \sqrt{100 - 56}}{4}$

= $\frac{10 \pm \sqrt{44}}{4}$

= $\frac{10 \pm 2 \sqrt{11}}{4}$

i.e. either $x = \frac{5 + \sqrt{11}}{2}$ or $x = \frac{5 - \sqrt{11}}{2}$