Question

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

Answer 1

Answer:

5+ square root of 33 over 2 (A)

Step-by-step explanation:

i just took the test and got it right!

Answer 2

Answer:

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

$x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$          ....[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

$x = \frac{-(-5) \pm \sqrt{(-5)^2-4(1)(-2)} }{2(1)}$

⇒$x = \frac{5 \pm \sqrt{25+8} }{2}$

Simplify:

$x = \frac{5 \pm \sqrt{33} }{2}$

Therefore, the exact solutions of the given equations are:

$x = \frac{5+\sqrt{33} }{2}$ and $x = \frac{5 -\sqrt{33} }{2}$