Answer:
x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74
Explanation:
Solve for x:
(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = 0
Simplify and substitute y = 4 - x.
(x - 4) (3 x - 2) - ((6 - 5 x) (x - 4) (8 x - 1))/(4 - x) = -434 + 257 (4 - x) - 37 (4 - x)^2
= -37 y^2 + 257 y - 434:
-37 y^2 + 257 y - 434 = 0
Divide both sides by -37:
y^2 - (257 y)/37 + 434/37 = 0
Subtract 434/37 from both sides:
y^2 - (257 y)/37 = -434/37
Add 66049/5476 to both sides:
y^2 - (257 y)/37 + 66049/5476 = 1817/5476
Write the left hand side as a square:
(y - 257/74)^2 = 1817/5476
Take the square root of both sides:
y - 257/74 = sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Add 257/74 to both sides:
y = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Substitute back for y = 4 - x:
4 - x = 257/74 + sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Subtract 4 from both sides:
-x = sqrt(1817)/74 - 39/74 or y - 257/74 = -sqrt(1817)/74
Multiply both sides by -1:
x = 39/74 - sqrt(1817)/74 or y - 257/74 = -sqrt(1817)/74
Add 257/74 to both sides:
x = 39/74 - sqrt(1817)/74 or y = 257/74 - sqrt(1817)/74
Substitute back for y = 4 - x:
x = 39/74 - sqrt(1817)/74 or 4 - x = 257/74 - sqrt(1817)/74
Subtract 4 from both sides:
x = 39/74 - sqrt(1817)/74 or -x = -39/74 - sqrt(1817)/74
Multiply both sides by -1:
Answer: x = 39/74 - sqrt(1817)/74 or x = 39/74 + sqrt(1817)/74