1)
Solve for x:
(x - 5)^2 = (2 x - 3)^2
Take the square root of both sides:
x - 5 = 2 x - 3 or x - 5 = 3 - 2 x
Subtract 2 x - 5 from both sides:
-x = 2 or x - 5 = 3 - 2 x
Multiply both sides by -1:
x = -2 or x - 5 = 3 - 2 x
Add 2 x + 5 to both sides:
x = -2 or 3 x = 8
Divide both sides by 3:
Answer: | x = -2 or x = 8/3
2)
Solve for x:
(x - 4) (x + 3) = (x - 2)^2
Expand out terms of the left hand side:
x^2 - x - 12 = (x - 2)^2
Expand out terms of the right hand side:
x^2 - x - 12 = x^2 - 4 x + 4
Subtract x^2 - 4 x + 4 from both sides:
3 x - 16 = 0
Add 16 to both sides:
3 x = 16
Divide both sides by 3:
Answer: | x = 16/3
3)
Solve for x:
5 x (6 x - 10) = -3 x (7 x - 2)
Expand out terms of the left hand side:
30 x^2 - 50 x = -3 x (7 x - 2)
Expand out terms of the right hand side:
30 x^2 - 50 x = 6 x - 21 x^2
Subtract 6 x - 21 x^2 from both sides:
51 x^2 - 56 x = 0
Factor x from the left hand side:
x (51 x - 56) = 0
Split into two equations:
x = 0 or 51 x - 56 = 0
Add 56 to both sides:
x = 0 or 51 x = 56
Divide both sides by 51:
Answer: | x = 0 or x = 56/51