(x-3)(x-4)=33/34

Question

which is the number of x?

Answer 1

33/34 is almost 1

Therefore, you can chage the given equation to (x-3)(x-4) = 1

Expand the left part of equation gives you x² -7x + 12 = 1

Finally you will get x2 -7x + 11 = 0 and now you can not factoring this equation. So, you have to use formula for qadratic equation

x = ( -b ± √(b² - 4 ac ) ) / 2a

if you substitute a, b and c to the formula

x = ( 7 ± √5 ) / 2  therefore  x = 4.618 or x = 2.382

This method will be much easier to solve and have very littel difference with solving 33/34.

If you solve with 33/34, solusion is x = 4.614 or x = 2.387

This is depening on the requirement of significant figures. If the problem wants more precise accuracy, you have to use 33/34 but calcuration with approximation, solving with 1 will be O.K.

Hope this will help you.

 

Answer 2

Expand the LHS,

x^2 - 7x + 12 = 33/34

Complete the square,

(x-3.5)^2 = 33/34-12+3.5^2 = 83/68

x = 3.5 +/- sqrt(83/68) <==Answer