1) x^2 - 9 + 14 = 0x^2 + 5 = 0x^2 = -5There are no real solutions to this equation.
2) (2x - 7)^2 = (2x - 1)^2Expanding both sides:(2x - 7)(2x - 7) = (2x - 1)(2x - 1)4x^2 - 28x + 49 = 4x^2 - 4x + 1We can simplify this to:-28x + 49 = -4x + 1Subtracting 4x from both sides:-32x + 49 = 1Subtracting 49 from both sides:-32x = -48Dividing by -32:x = 3/2
Therefore, the solution to the second equation is x = 3/2.
1) x^2 - 9 + 14 = 0
x^2 + 5 = 0
x^2 = -5
There are no real solutions to this equation.
2) (2x - 7)^2 = (2x - 1)^2
Expanding both sides:
(2x - 7)(2x - 7) = (2x - 1)(2x - 1)
4x^2 - 28x + 49 = 4x^2 - 4x + 1
We can simplify this to:
-28x + 49 = -4x + 1
Subtracting 4x from both sides:
-32x + 49 = 1
Subtracting 49 from both sides:
-32x = -48
Dividing by -32:
x = 3/2
Therefore, the solution to the second equation is x = 3/2.