Question

Solve the following equation 0 = -x^2 + 4x - 2

Answer 1

To solve the given equation we will use the quadratic formula:

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

In the given equation:

$\begin{gathered} a=-1, \\ b=4, \\ c=-2. \end{gathered}$

Substituting the above values in the formula, we get:

$x=\frac{-4\pm\sqrt{16-4(-1)(-2)}}{2(-1)}.$

Simplifying the above result, we get:

$x=\frac{-4\pm\sqrt{8}}{-2}=2\pm\sqrt{2}.$

Answer:

$\begin{gathered} x_1=2-\sqrt{2}\approx0.59, \\ x_2=2+\sqrt{2}\approx3.41. \end{gathered}$