Question

Find all real solutions of the equation.

$x^2-9x+14=0$

Short answer

Real solution of the given equation: $x=7,2$

Step-by-step solution

Step 1. Factorize the given equation.

Here we shall first find the factors of this quadratic equation.

$\begin{array}{c}{x}^2-9x+14=0\\ x^2-2x-7x+14=0\\ x\left(x-2\right)-7\left(x-2\right)=0\\ \left(x-7\right)\left(x-2\right)=0\end{array}$

Step 2. Now put each factor of the quadratic equation equal to 0.

$\begin{array}{l}\left(x-7\right)=0\\ \left(x-2\right)=0\end{array}$

Step 3. Simplify the equation.

We shall simplify both equations of the factors to determine 2 real solutions.

$\begin{array}{c}\left(x-7\right)=0\\ x=7\\ \left(x-2\right)=0\\ x=2\end{array}$