# How do you solve  -x^2 +2x +1 = 0 using the quadratic formula?

May 24, 2016

$x = \left\{- \sqrt{2} + 1 , \sqrt{2} + 1\right\}$

#### Explanation:

$- {x}^{2} + 2 x + 1 = 0$

$a {x}^{2} + b x + c = 0$

$\Delta = \sqrt{{b}^{2} - 4 \cdot a \cdot c}$

x=(-b±Delta)/(2a)

$a = - 1$
$b = 2$
$c = 1$

$\Delta = \sqrt{{2}^{2} + 4 \cdot 1 \cdot 1}$

$\Delta = \sqrt{4 + 4}$

$\Delta = \sqrt{8}$

$\Delta = 2 \sqrt{2}$

x_1=(-2-2sqrt2)/(2*(-1)

${x}_{1} = - 2 \frac{\left(1 + \sqrt{2}\right)}{- 2}$

${x}_{1} = 1 + \sqrt{2}$

${x}_{2} = \frac{- 2 + 2 \sqrt{2}}{- 2}$

${x}_{2} = \frac{- 2 \left(1 - \sqrt{2}\right)}{- 2}$

${x}_{2} = 1 - \sqrt{2}$