Answer:
Step-by-step explanation:
[tex](2x - 3)^{2} = 4x - 6[/tex]
Using FOIL, we can expand the polynomial on the left-hand side of the equation:
[tex]4x^{2} - 12x + 9 = 4x - 6[/tex]
Next, let's move all of the terms to the left-hand side of the equation and combine like terms:
[tex]4x^{2} - 12x - 4x + 9 + 6 = 0[/tex]
[tex]4x^{2} - 16x + 15 = 0[/tex]
Now we can factor the quadratic:
[tex](2x - 5)(2x - 3) = 0[/tex]
This produces two equations to give us the two solutions:
The first solution:
[tex]2x - 5 = 0[/tex]
[tex]2x = 5[/tex]
[tex]x = \frac{5}{2}[/tex]
and the second solution:
[tex]2x - 3 = 0[/tex]
[tex]2x = 3[/tex]
[tex]x = \frac{3}{2}[/tex]
So the solutions to this problem are [tex]x = \frac{3}{2}, \frac{5}{2}[/tex]
