How do you factor 2x squared plus 3x equals 3x minus 1 squared minus x squared?

Answer 1

If you mean

2x2 + 3x = (3x - 1)2 - x2

Then you can solve it this way:

Expand:

2x2 + 3x = 9x2 - 6x + 1 - x2

Group like terms:

2x2 + 3x = 8x2 - 6x + 1

6x2 - 9x - 1 = 0

Complete the square:

6x2 - 9x = 1

x2 - 3x/2 = 1/6

x2 - 3x/2 + 9/16 = 1/6 + 9/16

(x - 3/4)2 = 8/48 + 27/48

(x - 3/4)2 = 35/48

Solve for x:

x - 3/4 = ± √(35/48)

x - 3/4 = ± √(35/3) / 4

x = 3/4 ± √(35/3) / 4

x = [3 ± √(35/3)] / 4

If you mean something else, then you'll need to be clearer with your question.