Question

Complete the square 2m2−3m=−50

Answer 1

Answer:

Completing the square answer

$\left(m - \frac{3}{4}\right)^2 = - \frac{391}{16}$

Solution set

$m = \frac{3}{4} + \frac{\sqrt[]{391}i}{4} = 0.75 + 4.94343 \, i$

$m = \frac{3}{4} - \frac{\sqrt[]{391}i}{4}$ = $0.75 - 4.94343 \, i$

Step-by-step explanation:

Assuming the question is correctly interpreted as 2m2 = 2m², here is how to proceed

We have $2m^2 - 3m =-50$

Divide by 2 on both sides

$m^2 - \frac{3}{2}m = - 25$

Take half of the  coefficient of $x$ and square it

$\left[ - \frac{3}{2} \cdot \frac{1}{2} \right]^2 = \frac{9}{16}$

Add the result to both sides

$m^2 - \frac{3}{2}m + \frac{9}{16} = - 25 + \frac{9}{16}$

$m^2 - \frac{3}{2}m + \frac{9}{16}$ can be re-written as a perfect square

$\left(m - \frac{3}{4}\right)^2$

The RHS becomes

$- 25 + \frac{9}{16} = \frac{(-25)(16) + 9}{9} = \frac{-391}{16}$

Therefore,

$\left(m - \frac{3}{4}\right)^2 = - \frac{391}{16}$

Take the square root of both side

$m - \frac{3}{4} = \pm \sqrt[]{ - \frac{391}{16}}$

Simplify

$m - \frac{3}{4} = \pm \frac{\sqrt[]{391}i}{4}$

Adding $\frac{3}{4}$ both sides

$m = \frac{3}{4} + \frac{\sqrt[]{391}i}{4}$

This gives the two solutions

$m= \frac{3}{4} + \frac{\sqrt[]{391}i}{4}$  and

$m = \frac{3}{4} - \frac{\sqrt[]{391}i}{4}$

which becomes

$m = 0.75 + 4.94343 \, i$ and

$m = 0.75 - 4.94343 \, i$