Question

Solve the following quadratic equations by factorization:
(x-5)(x-6)=25/(24)²

Answer 1

The solved value of x in the given quadratic equation are $\frac{145}{24}$ and $\frac{119}{24}$

Step-by-step explanation:

Given equation is $(x-5)(x-6)=\frac{25}{24^2}$

To solve the given equation by Factorization method :

• $(x-5)(x-6)=\frac{25}{24^2}$
• $(x-5)(x-6)=\frac{25}{576}$
• $x(x-6)-5(x-6)=\frac{25}{576}$
• $x(x)-x(6)-5(x)-5(-6)=\frac{25}{576}$
• $x^2-6x-5x+30=\frac{25}{576}$
• $x^2-6x-5x+30=\frac{25}{576}$
• $x^2-11x+30=\frac{25}{576}$
• $x^2-10x-x+25+5=\frac{25}{576}$

• $x^2-10x+25-(x-5)=\frac{5^2}{24^2}$ 
• $(x-5)^2-(x-5)-(\frac{5}{24})^2=0$

Let a=x-5

• Then the above equation becomes
•  $a^2-a-(\frac{5}{24})^2=0$
• $a^2-\frac{25a}{24}+\frac{y}{24}-\frac{5^2}{24^2}=0$
• $a(a-\frac{25}{24})(\frac{1}{24})(a-\frac{25}{24})=0$

• $(a-\frac{25}{24})(a+\frac{1}{24})=0$

$(a-\frac{25}{24})=0$ or $(a+\frac{1}{24})=0$

• $a=\frac{25}{24}$
• $x-5=\frac{25}{24}$ ( since a=x-5)
• $x=\frac{25}{24}+5$
• $x=\frac{25+24(5)}{24}$
• $x=\frac{25+120}{24}$
• $x=\frac{145}{24}$

 Now $(a+\frac{1}{24})=0$

• $a=-\frac{1}{24}$
• $x-5=-\frac{1}{24}$
• $x=\frac{-1}{24}+5$
• $x=\frac{-1+5(24)}{24}$
• $x=\frac{-1+120}{24}$
• $x=\frac{119}{24}$

Therefore the values of x are $\frac{145}{24}$ and $\frac{119}{24}$