How do you solve for x ?
#(x-2)(x-3)=34/33^2#

Question

Eva Abramson · Accepted Answer

#100/33 " and " 65/33#

#(x-2)(x-3) = 34/33^2# #=> (33x-66)(33x-99) = 34#

being hopeful that #(33x-66) and (33x-99)# are integers , at this point, I note that this equation is basically a factorization of 34 such that #a.b=34# and #a-b = 33#

Of course, 34 and 1 or (-1) and (-34) are the factors.

There are two possibilities:

Case I : #a=34 and b =1\ => x = 100/33#

Case II : #a=-1 and b = -34 \ => x= 65/33#

Avery Alexander · Answer

#x=65/33 or 100/33#

Assuming x-3 = a, x-2 = a+1

#(x-2)(x-3)=(33+1)/33^2#

#=>(a+1)a=33/33^2+1/33^2#

#=>a^2+a-1/33^2-1/33=0#

#=>(a+1/33)(a-1/33)+1(a-1/33)=0#

#=>(a-1/33)(a+1/33+1)=0#

#=>(a-1/33)(a+34/33)=0#

#a=1/33 and a=-34/33#

when #a=1/33#

then # x-3=1/33#

#x=3+1/33=100/33#

when #a=-34/33#

then # x-3=-34/33#

# x=3-34/33=(99-34)/33=65/33#

Kennedy Adams · Answer

undefined To solve for x in the equation (x-2)(x-3) = 34/33^2, we can start by expanding the left side of the equation:

(x-2)(x-3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6

Now, we can set this expression equal to 34/33^2:

x^2 - 5x + 6 = 34/33^2

To simplify the equation, we can multiply both sides by 33^2 to eliminate the fraction:

33^2(x^2 - 5x + 6) = 34

Expanding the left side of the equation:

33^2x^2 - 5(33^2)x + 6(33^2) = 34

This simplifies to a quadratic equation:

1089x^2 - 165x + 6534 = 34

Rearranging the equation:

1089x^2 - 165x + 6500 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula.

How do you solve for x ? #(x-2)(x-3)=34/33^2#