Question

When $7$ is subtracted from the square of a number, the result is $6$ times the number. Find a positive solution.

Answer 1

Step1: Find the solution of quadratic equation.

Let the number be $m$.

According to the question,

$$\begin{gathered} m^2-7=6m \\ \Rightarrow m^2-6m-7=0 \\ \Rightarrow m^2-7m+m-7=0 \\ \Rightarrow m(m-7)+1(m-7)=0 \\ \Rightarrow (m-7)(m+1)=0 \\ \Rightarrow m-7=0orm+1=0 \\ \therefore m=7orm=-1 \end{gathered}$$

Hence, the positive solution is $7$.