Answer:
[tex]-3 ± 2\sqrt{3} = x[/tex]
Step-by-step explanation:
x² + 6x + 9 = 12 → x² + 6x - 3
Since this Quadratic Expression is unfactorable, apply the Quadratic Formula:
[tex]x = -b ± \frac{\sqrt{{b}^{2} - 4ac}}{2a}[/tex]
[tex] -6 ± \frac{\sqrt{{6}^{2} - 4(1)(-3)}}{2(1)} = -6 ± \frac{\sqrt{36 + 12}}{2} = -6 ± \frac{\sqrt{48}}{2} \\ \\ -3 ± 2\sqrt{3}[/tex]
√48 = √[3 × 16] = 4√3
½[4√3] = 2√3
Then attach half of -6 to it as well [-3]:
-3 ± 2√3
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