[tex]a) {(x - 2)}^{2} - {(x + 1)}^{2} = x - 4[/tex]
[tex] {x}^{2} - 4x + 4 - {x}^{2} - 2x - 1 = x - 4[/tex]
[tex] - 4x - 2x - x = - 4 - 4 + 1[/tex]
[tex] - 7x = - 7 \: | \div ( - 7)[/tex]
[tex]x = 1[/tex]
[tex]b) {(2x + 3)}^{2} + 7 = 4 {(x - 2)}^{2} [/tex]
[tex]4 {x}^{2} + 12x + 9 + 7 = 4 {x}^{2} - 16x + 16[/tex]
[tex]12x + 16x = 16 - 9 - 7[/tex]
[tex]28x = 0[/tex]
[tex]x = 0 \div 28[/tex]
[tex]x = 0[/tex]
[tex]c) {(3x + 4)}^{2} + 20 = 5 {(x + 1)}^{2} + {(2x - 3)}^{2} [/tex]
[tex]9 {x}^{2} + 24x + 16 + 20 = 5 {x}^{2} + 10x + 5 + 4 {x}^{2} - 12x + 9[/tex]
[tex]24x - 10x + 12x = 5 + 9 - 16 - 20[/tex]
[tex]26x =- 22[/tex]
[tex]x =- \frac{22}{26} [/tex]
[tex]x = -\frac{11}{13} [/tex]
