Question

$(x-3)(x-4)=\frac{34}{{33}^2}$.Solve

Answer 1

Simplification of quadratic equation:

The given equation is,

$$\begin{gathered} (x-3)(x-4)=\frac{34}{{33}^2} \\ \Rightarrow (x-3)(x-4)=\frac{34}{1089} \\ \Rightarrow x^2-7x+12=\frac{34}{1089} \\ \Rightarrow x^2-7x+12-\frac{34}{1089}=0 \\ \Rightarrow 1089x^2-7623x-13034=0 \\ \Rightarrow 1089x^2-33\times 133x-33\times 98x-13034=0 \\ \Rightarrow \left(33x-98\right)\left(33x-133\right)=0 \\ \therefore x=\frac{98}{33},\frac{133}{33} \end{gathered}$$

Thus, the solution is $\mathit{x}\mathbf{=}\frac{\mathbf{98}}{\mathbf{33}}\mathbf{,}\frac{\mathbf{133}}{\mathbf{33}}$.