Question

What are the exact solutions of x2 = 5x + 2?

Answer 1

5+ square root of 33 over 2 (A)

Explanation:

i just took the test and got it right!

Answer 2

A quadratic equation
`ax^2+bx+c = 0` ,....[1] then the solution of this is given by:

`x = (-b \pm √(b^2-4ac) )/(2a)` ....[2]

Given the quadratic equation:

`x^2=5x+2`

We can write this as:

`x^2-5x-2 =0`

On comparing with [1] we have;

a = 1, b = -5 and c = -2

Substitute these in [2] we have

`x = (-(-5) \pm √((-5)^2-4(1)(-2)) )/(2(1))`

⇒
`x = (5 \pm √(25+8) )/(2)`

Simplify:

`x = (5 \pm √(33) )/(2)`

Therefore, the exact solutions of the given equations are:

`x = (5+√(33) )/(2)` and
`x = (5 -√(33) )/(2)`