Question

Solve By Completing the Square. Give Exact Answer Only.

2w^2 - 3w = 4

Answer 1

\[2w^2-3w=4\]
Divide both sides by 2 to get the coefficient of w^2 to 1.
\[w^2-\frac{3}{2}w=2\]
Completing the square is essentially \[(x-a)^2 = x^2-2ax+a^2\]
what you have is a part of the right side of that expression.
\[(x-a)^2 = x^2-2ax+a^2=x^2-\frac{3}{2}x+a^2\]
So now, you have to find what that a value is.
looking at the \[-2ax=-\frac{3}{2}x\], you can find that the a value is 3/4.
Plug it back into the equation and you get \[(x-\frac{3}{4})^2 = x^2-\frac{3}{2}x+\frac{9}{4}\]
Notice how you have an extra term in there. To make up for adding that term, simply subtract it from the expression.
\[(x-\frac{3}{4})^2-\frac{9}{4}=x^2-\frac{3}{2}x+\frac{9}{4}-\frac{9}{4}=x^2-\frac{3}{2}x\]
So your final equation just needs to simplify
\[(x-\frac{3}{4})^2-\frac{9}{4}=2\]