How do you solve x²-7x+4=0 using the quadratic formula?

May 10, 2016

Answer:

$x = \frac{7}{2} \pm \frac{\sqrt{33}}{2}$

Explanation:

${x}^{2} - 7 x + 4 = 0$ is in the form $a {x}^{2} + b x + c = 0$ with $a = 1$, $b = - 7$ and $c = 4$.

This has roots given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

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

$= \frac{7 \pm \sqrt{49 - 16}}{2}$

$= \frac{7 \pm \sqrt{33}}{2}$

$= \frac{7}{2} \pm \frac{\sqrt{33}}{2}$