Question

Solve for x in the equation x2+20x+100=36

Answer 1

The answer is:

`x = - 64 / 22 = -2.909091`
But if x2 was supposed to be x^2 then the answer is:

`x = - 4.-16`

Answer 2

x = -4 and x = -16.

Explanation:

We have the equation,

`x^(2)+20x+100=36`

i.e.
`x^(2)+20x+64=0`

As the solution of a quadratic equation
`ax^(2)+bx+c=0` is given by
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`.

On comparing, a = 1, b = 20, c = 64.

So, the solution is,

`x=\frac{-20\pm \sqrt{(20)^(2)-4* 1* 64}}{2a* 1}`.

i.e.
`x=(-20\pm √(400-256))/(2)`.

i.e.
`x=(-20\pm √(144))/(2)`.

i.e.
`x=(-20\pm 12)/(2)`.

i.e.
`x=(-20+12)/(2)` and
`x=(-20-12)/(2)`.

i.e.
`x=(-8)/(2)` and
`x=(-32)/(2)`.

i.e. x = -4 and x = -16

Thus, the solution of the given equation is x = -4 and x = -16.