[tex] x^{2} +12x+30=0[/tex]
we first complete the square, by writing 12 as 2*6, then adding and subtracting [tex]6^{2} =36[/tex]
[tex](x^{2} +12x+36)-36+30=0[/tex]
[tex](x+6)^{2} -36+30=0[/tex]
[tex](x+6)^{2} -6=0[/tex]
[tex](x+6)^{2} =6[/tex]
Solution:
take the square root of both sides
[tex] \sqrt{(x+6)^{2} } = \sqrt{6} [/tex]
[tex]|(x+6)|= \sqrt{6}[/tex] because [tex] \sqrt{ A^{2} }=|A|[/tex]
then
i) [tex]x+6= \sqrt{6} [/tex], so [tex]x= -6+\sqrt{6}[/tex]
ii) [tex]x+6= -\sqrt{6}[/tex] so [tex]x= -6-\sqrt{6}[/tex]
Solution: x∈{[tex]x= -6+\sqrt{6}[/tex], [tex]x= -6-\sqrt{6}[/tex]}
