Question

How do you solve `x^2= 8- 5x`?

Answer 1

`x = (-5 +- sqrt(57))/2`

Explanation:

The first thing to do is to convert the equation to standard form `y = ax^2 + bx + c`. In this case of our equation, it is `x^2 + 5x - 8 = 0`.

By using this, we know the following
`a = 1`
`b = 5`
`c = -8`

In order to find the value of `x` in the equation above, we need to substitute these values to the quadratic formula `x = (-b +- sqrt(b^2 - 4ac))/ (2a)`

In this case

`x = (-5 +- sqrt(5^2 - 4(1)(-8)))/ (2(1))`
`x = (-5 +- sqrt(25 - (-32)))/2`
`x = (-5 +- sqrt(57))/2`

So we know that `x = (-5 +- sqrt(57))/2`