Question

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

Answer 1

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

Answer 2

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=(-b\pm√(b^2-4ac))/(2a)`
In this case, a = 2, b = -2, and c = -1. Let's plug these in.


Simplify...

`x=\frac{2\pmsqrt{4+8}}4`


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


`√(12)=√(2*2*3)=2√(3)`


`x=\frac{2\pm2√(3)}4`


`x=\frac{1\pm√(3)}2`


`\boxed{x=\frac{1+√(3)}2\ or\ \frac{1-√(3)}2}`