cum rezolv ecuatiile:
[tex] a){x }^{2} + 6x = 16 \\ b) {x}^{2} - 2x = 8 \\ c)4 {x}^{2} - 4x = 12[/tex]

[tex]a) {x}^{2} + 6x = 16[/tex]

[tex] {x}^{2} + 6x - 16 = 0[/tex]

[tex] {x}^{2} + 8x - 2x - 16 = 0[/tex]

[tex]x(x + 8) - 2(x + 8) = 0[/tex]

[tex](x + 8)(x - 2) = 0[/tex]

[tex]x +8 = 0 = > x_{1} = -8[/tex]

[tex]x - 2 = 0 = > x_{2} = 2[/tex]

[tex]b) {x}^{2} - 2x = 8[/tex]

[tex] {x}^{2} - 2x - 8 = 0[/tex]

[tex] {x}^{2} - 4x + 2x - 8 = 0[/tex]

[tex]x(x - 4) + 2(x - 4) = 0[/tex]

[tex](x - 4)(x + 2) = 0[/tex]

[tex]x - 4 = 0 = > x_{1} = 4[/tex]

[tex]x + 2 = 0 = > x_{2} = - 2[/tex]

[tex]c)4{x}^{2} - 4x = 12[/tex]

[tex]4 {x}^{2} - 4x - 12 = 0 \: | \div 4[/tex]

[tex] {x}^{2} - x - 3 = 0[/tex]

[tex]a = 1 [/tex]

[tex]b = - 1[/tex]

[tex]c = - 3[/tex]

[tex]\Delta = {b}^{2} - 4ac[/tex]

[tex]\Delta = {( - 1)}^{2} - 4 \times 1 \times ( - 3)[/tex]

[tex]\Delta = 1 + 12[/tex]

[tex]\Delta = 13 [/tex]

[tex]x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}[/tex]

[tex]x_{1,2}=\frac{-( - 1)\pm\sqrt{13}}{2 \times 1}[/tex]

[tex]x_{1,2}=\frac{1\pm\sqrt{13}}{2}[/tex]

[tex]x_{1}=\frac{1 + \sqrt{13}}{2}[/tex]

[tex]x_{2}=\frac{1 - \sqrt{13}}{2}[/tex]