1)
⇒ x² - 6x = -8
[tex]\sf add \ 9 \ on \ both \ sides[/tex]
⇒ x² - 6x + 9 = -8 + 9
[tex]\sf simplify \ and \ complete \ square[/tex]
⇒ x² - 3x - 3x + 9 = 1
[tex]\sf factor \ common \ term[/tex]
⇒ x(x - 3) - 3(x - 3) = 1
[tex]\sf collect \ into \ groups[/tex]
⇒ (x - 3)² = 1
[tex]\sf square \ root \ both \ sides[/tex]
⇒ x - 3 = ±√1
[tex]\sf simplify[/tex]
⇒ x - 3 = ±1
[tex]\sf change \ side[/tex]
⇒ x = 1 + 3, -1 + 3
[tex]\sf simplify[/tex]
⇒ x = 4, 2
2)
[tex]\rightarrow \sf 4x^2 + 12x + 11 = 0[/tex]
[tex]\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}\right) = 0[/tex]
[tex]\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}+\left(\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2\right) = 0[/tex]
[tex]\rightarrow \sf 4\left(x+\dfrac{3}{2}\right)^2+2 = 0[/tex]
[tex]\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{2}{4}[/tex]
[tex]\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{1}{2}[/tex]
[tex]\rightarrow \sf x+\dfrac{3}{2} = \pm \sqrt{-\dfrac{1}{2} }[/tex]
[tex]\rightarrow \sf x+\dfrac{3}{2} = \pm i\sqrt{\dfrac{1}{2} }[/tex]
[tex]\rightarrow \sf x= \pm i\sqrt{\dfrac{1}{2} }-\dfrac{3}{2}[/tex]
