Answer:
[tex]x = \frac{5}{2} \: \: \: \: \: \: \: \: and \: \: \: \: x = - \frac{1}{2} \\ [/tex]
Step-by-step explanation:
[tex]4(x - 1)^2 - 9 = 0\\ ((4)x {}^{2} - 2x + 1) - 9 = 0 \\ 4x {}^{2} - 8x + 4 - 9 = 0 \\ 4x {}^{2} - 8x - 5 = 0 \\ 4x {}^{2} + 2x - 10x - 5 = 0 \\ 2x(2x + 1) - 5(2x + 1) = 0 \\ (2x - 5)(2x + 1) = 0 \\ 2x - 5 = 0 \: \: \: \: \: \: \: and \: \: \: \: \: 2x + 1 = 0 \\ x = \frac{5}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: and \: \: \: \: x = - \frac{1}{2} [/tex]
