# How do you solve using the completing the square method  x^2 – 4x + 1 = 0?

Mar 7, 2016

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

#### Explanation:

Given equation is ${x}^{2} - 4 x + 1 = 0$

${x}^{2} - 4 x = - 1$--------(1)

third term =(1/2 xx  coefficient of x )^2

$t h i r d t e r m = {\left(\frac{1}{2} \times - 4\right)}^{2}$

$t h i r d t e r m = {\left(- 2\right)}^{2}$

$t h i r d t e r m = 4$

Add 4 to both sides of equation 1

${x}^{2} - 4 x + 4 = - 1 + 4$

${\left(x - 2\right)}^{2} = 3$

$\left(x - 2\right) = \pm \sqrt{3}$

$x = 2 \pm \sqrt{3}$

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