[tex] x^2 + 3x - 3 = 0 [/tex]
[tex] x^2 + 3x = 3 [/tex]
[tex] x^2 + 3x + \left( \dfrac{3}{2} \right)^2 = 3 + \left( \dfrac{3}{2} \right)^2 [/tex]
[tex] \left(x + \dfrac{3}{2} \right)^2 = \dfrac{12}{4} + \dfrac{9}{4} [/tex]
[tex] \left(x + \dfrac{3}{2} \right)^2 = \dfrac{21}{4} [/tex]
[tex] x + \dfrac{3}{2} = \pm \dfrac{\sqrt{21}}{2} [/tex]
[tex] x + \dfrac{3}{2} = \dfrac{\sqrt{21}}{2} [/tex] or [tex] x + \dfrac{3}{2} = -\dfrac{\sqrt{21}}{2} [/tex]
[tex] x = \dfrac{\sqrt{21}}{2} - \dfrac{3}{2} [/tex] or [tex] x = -\dfrac{\sqrt{21}}{2} - \dfrac{3}{2} [/tex]
