Maria looks at the equation (x - 5)(x - 6) = 2 and says that since the equation is in factored form it can be solved as follows: (x - 5)(x - 6) = 2 x - 5 = 2 and x - 6 = 2 x = 7 and x = 8 Explain to Maria why this is incorrect and explain to her the correct way to solve the equation

We have been given that Maria looks at the equation [tex](x - 5)(x - 6) = 2[/tex] and says that since the equation is in factored form it can be solved as follows:

[tex]x - 5=2\text{ and }x - 6= 2[/tex]

[tex]x=7\text{ and }x=8[/tex]

We are asked to explain why Maria's work is incorrect and what is the correct way to solve the equation.

We know that factored form of an equation is [tex](x-a)(x-b)=0[/tex]. There should be 0 on right side of equation.

Since equation [tex](x - 5)(x - 6) = 2[/tex] has 2 on right side, therefore, it is not is factored form.

First of all, we will expand left side of equation as:

[tex]x(x-6)-5(x-6)= 2[/tex]

[tex]x^2-6x-5x+30= 2[/tex]

[tex]x^2-11x+30= 2[/tex]

Upon subtracting 2 from both sides, we will get:

[tex]x^2-11x+30-2= 2-2[/tex]

[tex]x^2-11x+28=0[/tex]

Upon splitting the middle term, we will get:

[tex]x^2-7x-4x+28=0[/tex]

[tex]x(x-7)-4(x-7)=0[/tex]

[tex](x-7)(x-4)=0[/tex]

Using zero product property, we will get:

[tex]x-7=0\text{ or }x-4=0[/tex]

[tex]x=7\text{ or }x=4[/tex]

Therefore, the solutions for our given equation are [tex]x=4,7[/tex].