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 \(x = \frac{5 -\sqrt{33} }{2}\)
