Question

5m² – 2m = 2

Answer 1

Given: 5m² – 2m = 2
On rewriting this equation in the standard form of the quadratic equation, we get:
5m² – 2m – 2 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 5, b = –2 and c = –2
Here, the variable is m.
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 5, b = –2 and c = –2, we get:
$$\begin{gathered} m=\frac{-\left(-2\right)\pm \sqrt{{\left(-2\right)}^2-4\times 5\times \left(-2\right)}}{2\times 5} \\ =\frac{2\pm \sqrt{4+40}}{10} \\ =\frac{2\pm \sqrt{44}}{10} \\ =\frac{2\pm 2\sqrt{11}}{10} \\ =\frac{2\left(1\pm \sqrt{11}\right)}{10} \\ =\frac{1\pm \sqrt{11}}{5} \end{gathered}$$
Thus, the solution of the given quadratic equation is m = $\frac{1+\sqrt{11}}{5},\frac{1-\sqrt{11}}{5}$.