2230.11 – DON'T GUESS!

Given that $(y + 1) (2y - 3) = 25$ , what is y?

And DON’T GUESS!

Solution

Playing it straight, multiply out. The equation

$(y + 1) (2y - 3) = 25,$

becomes

$2 y^2 - 3y + 2y - 3 = 25,$

which becomes

$0 = 2 y^2 - y - 28 = (y - 4) (2y + 7).$

So either $y$ is 4 or -7/2.

We might have hoped, looking at the original equation and noticing that $25 = 5 \times 5$ , that perhaps $y + 1 = 5$ and $2y - 3 = 5$ . This would give us $y = 4$ but misses $y = -7/2$ .