Question

will medal
Solve 2x2 − 6x = −8.

negative 3 plus or minus 5i all over 2
the quantity of 3 plus or minus 2i square root 30 all over 2
the quantity of 3 plus or minus i square root 30 all over 2
the quantity of 3 plus or minus i square root 7 all over 2

Answer 1

Lets complete the square and find out

We need to x^2 term to have a coefficient of 1...so lets divide everything by 2

\[\large x^2 - 3x = -4\]

Now...lets take half the coefficient of the 'x' term....so 3/2 and square that....so 9/4...and add this to both sides of our equation

\[\large x^2 - 3x + \frac{9}{4} = -4 + \frac{9}{4}\]

Simplify the right hand side...and turn the left hand side into a square

\[\large (x - \frac{3}{2})^2 = -\frac{7}{4}\]

Take the square root of both sides

\[\large x - \frac{3}{2} = \sqrt{-\frac{7}{4}}\]

Add \(\large \frac{3}{2}\) to both sides

\[\large x = \frac{3}{2} \pm \sqrt{-\frac{7}{4}}\]

Which can then be written as

\[\large x = \frac{3}{2} \pm \frac{\sqrt{-7}}{2}\]

Now how else can we simplify that?

Answer 2

by adding them ?