Question

What is the positive solution to the equation 0 = –x2 + 2x + 1?

Answer 1

Answer:

1±√2

Step-by-step explanation:

To solve the quadratic, use the quadratic formula. Substitute a = -1, b = 2 and c = 1.

The quadratic formula is $x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$.  

Substitute and you'll have:  

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-2+/-\sqrt{2^2-4(-1)(1)} }{2(-1)}=\frac{-2+/-\sqrt{4+4} }{-2)}$  

$\frac{-2+/-\sqrt{8} }{-2}=\frac{-2+/-2\sqrt{2} }{-2} = 1 +/- \sqrt{2}$