Question

Solve each problem by using the quadratic formula. Write solutions in simplest radical form. 2x2 – 2x – 1 = 0

Answer 1

When you have a quadratic in the form ax² + bx + c = 0, you can solve for x using the quadratic formula, which is as follows:
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
In this case, a = 2, b = -2, and c = -1. Let's plug these in.
$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(2)(-1)}{2(2)}$
Simplify...
$x=\frac{2\pmsqrt{4+8}}4$

$x=\frac{2\pmsqrt{12}}4$

$\sqrt{12}=\sqrt{2\times2\times3}=2\sqrt{3}$

$x=\frac{2\pm2\sqrt{3}}4$

$x=\frac{1\pm\sqrt{3}}2$

$\boxed{x=\frac{1+\sqrt{3}}2\ or\ \frac{1-\sqrt{3}}2}$

Answer 2

2x² - 2x - 1 = 0
x = -(-2) ± √((-2)² - 4(2)(-1))
                     2(2)
x = 2 ± √(4 + 8)
              4
x = 2 ± √(12)
            4
x = 2 ± 2√(3)
            4
x = 1 ± √(3)
           2
x = 1 + √(3)    U    x = 1 - √(3)
           2                          2