Second equation: (x - 5)^2 = 3x^2 - x + 14 Expanding the left side: (x - 5)(x - 5) = x^2 - 10x + 25 x^2 - 10x + 25 = 3x^2 - x + 14 Subtract x^2 from both sides and add x and -25 to both sides: 0 = 2x^2 + 9x - 11
So the solutions to the equations are: 2x^2 + 4x - 5 = 0 2x^2 + 9x - 11 = 0
First equation:
2(5x - 7x) = 2x^2 - 5
10x - 14x = 2x^2 - 5
-4x = 2x^2 - 5
0 = 2x^2 - 5 + 4x
0 = 2x^2 + 4x - 5
Second equation:
(x - 5)^2 = 3x^2 - x + 14
Expanding the left side:
(x - 5)(x - 5) = x^2 - 10x + 25
x^2 - 10x + 25 = 3x^2 - x + 14
Subtract x^2 from both sides and add x and -25 to both sides:
0 = 2x^2 + 9x - 11
So the solutions to the equations are:
2x^2 + 4x - 5 = 0
2x^2 + 9x - 11 = 0