Question

Solve this quadratic equation. x ^2 + 2x - 22 = 0

Answer 1

`x=-1+√(23)\; ,\;-1-√(23)`

Explanation:

Roots of quadratic equations
`ax^(2)+bx+c=0` calculated as:

`x=\frac{-b\pm\sqrt{b^(2)-4ac}}{2a}`

First, compare
`ax^(2)+bx+c=0` with
`x^(2)+2x-22=0`

here a = 1 , b = 2 and c = -22

Now, plug the value of a,b and c in
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`

`x=\frac{-2\pm \sqrt{2^(2)-4(1)(-22)}}{2(1)}`

`x=(-2\pm √(4+88))/(2)`

`x=(-2\pm √(92))/(2)`

`x=(-2\pm 2√(23))/(2)`

`x=-1\pm √(23)`

Hence,
`x=-1+√(23)\; ,\;-1-√(23)`