Question

Solve:$(x-5)(x-6)=\frac{25}{(24{)}^2}$

Answer 1

Given the equation,

$(x-5)(x-6)=\frac{25}{{24}^2}\Rightarrow x^2-11x+30=\frac{25}{576}\Rightarrow x^2-11x+30-\frac{25}{576}=0\Rightarrow x^2-\frac{264}{24}x+\frac{17280-25}{576}=0\Rightarrow x^2-\frac{264}{24}x+\frac{17255}{24\times 24}=0\Rightarrow x^2-(\frac{145}{24}+\frac{119}{24})x+(\frac{145}{24}\times \frac{119}{24})=0\Rightarrow x^2-\frac{145}{24}x-\frac{119}{24}x+(\frac{145}{24}\times \frac{119}{24})=0\Rightarrow x(x-\frac{145}{24})-\frac{119}{24}(x-\frac{145}{24})=0\Rightarrow (x-\frac{145}{24})(x-\frac{119}{24})=0\therefore x-\frac{145}{24}=0,x-\frac{119}{24}=0\Rightarrow x=\frac{145}{24},x=\frac{119}{24}\Rightarrow x=6\frac{1}{24},x=4\frac{23}{24}\therefore x=6\frac{1}{24},4\frac{23}{24}$