Question

X² - 6x + 4 = 0 solve and show work. ...?

Answer 1

The answer is 3 + √5 and 3 - √5.

This is quadratic equation: x² - 6x + 4 = 0
The general quadratic equation is ax² + bx + c = 0
Our equation can be rewritten: 1x² + (-6)x + 4 = 0
So, in our equation we have: a = 1, b = -6, c = 4

Now, x can be calculated using the formula:$x_{1,2}= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a}$
$x_{1,2} =\frac{-(-6)+/- \sqrt{ (-6)^{2}-4*1*4 } }{2*1} = \frac{6+/- \sqrt{36-16} }{2} = \frac{6+/- \sqrt{20} }{2} =\frac{6+/- \sqrt{4*5} }{2}= \\ =\frac{6+/- \sqrt{4}* \sqrt{5} }{2} =\frac{2*3+/- 2\sqrt{5} }{2}= \frac{2(3+/- \sqrt{5}) }{2} =3+/- \sqrt{5}$

From here:
$x_{1} =3+ \sqrt{5} \\ x_{2} =3- \sqrt{5}$