Question

Solve the equation by factorization: $x^2-10x+21=0$.

Answer 1

Step 1: Factorize the given equation.

Given equation: $x^2-10x+21=0$.

$$\begin{gathered} x^2-10x+21=0 \\ \Rightarrow x^2-7x-3x+21=0 \\ \Rightarrow x\left(x-7\right)-3\left(x-7\right)=0 \\ \Rightarrow \left(x-7\right)\left(x-3\right)=0 \end{gathered}$$

Step 2: Determine the roots of the equation.

Thus, the given equation can be written as, $\left(x-7\right)\left(x-3\right)=0$

So, either,

$$\begin{gathered} \left(x-7\right)=0 \\ \Rightarrow x=7 \end{gathered}$$

Or,

$$\begin{gathered} \left(x-3\right)=0 \\ \Rightarrow x=3 \end{gathered}$$

Therefore, the solutions to the given quadratic equation are $\mathit{x}\mathbf{=}\mathbf{7}$ and $\mathit{x}\mathbf{=}\mathbf{3}$.