Question

In the following exercises, solve:

$y^2=y+132$.

Short answer

The solution for the equation is,

$$\begin{gathered} y=12, \\ y=-11 \end{gathered}$$

Step-by-step solution

Step 1. Given Information.

The equation is,

$y^2=y+132$.

Step 2. Finding the solution.

$$\begin{gathered} y^2=y+132 \\ \Rightarrow y^2-y-132=0 \end{gathered}$$

Splitting the middle term such that the sum of the terms is $(-1)$and the product of the terms is $(-132)$,

$$\begin{gathered} \Rightarrow y^2-12y+11y-132=0 \\ \Rightarrow (y^2-12y)+(11y-132)=0 \\ \Rightarrow y(y-12)+11(y-12)=0 \\ \Rightarrow (y-12)(y+11)=0 \\ \Rightarrow y-12=0 \end{gathered}$$

or, $$\begin{gathered} y+11=0 \\ \Rightarrow y=12 \end{gathered}$$

or,$y=-11$.