Question

What are the exact solutions of x2 − 5x − 1 = 0?

x = the quantity of 5 plus or minus the square root of 29 all over 2

x = the quantity of negative 5 plus or minus the square root of 29 all over 2

x = the quantity of 5 plus or minus 2 times the square root of 5 all over 2

x = the quantity of negative 5 plus or minus 2 times the square root of 5 all over 2

Answer 1

x = the quantity of 5 plus or minus the square root of 29 all over 2

Answer 2

Using the quadratic formula:
\[x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
\[x = \frac{-(-5) \pm \sqrt{(-5)^2-4(1)(-1)}}{2 \times 1}\]
\[x = \frac{5 \pm \sqrt{25+4}}{2}\]
\[x = \frac{5 \pm \sqrt{29}}{2}\]