Answer:
[tex]\Huge \boxed{{x=-1\pm \sqrt{7}}}[/tex]
Step-by-step explanation:
x² + 2x = 6
Subtract both sides by 6.
x² + 2x - 6 = 0
ax²+bx+c=0
a=1, b=2, and c=-6
We can apply the quadratic formula.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Plug in the values.
[tex]\displaystyle x=\frac{-2\pm\sqrt{2^2-4(1)(-6)}}{2(1)}[/tex]
Evaluate.
[tex]\displaystyle x=\frac{-2\pm\sqrt{4-(-24)}}{2}[/tex]
[tex]\displaystyle x=\frac{-2\pm\sqrt{28}}{2}[/tex]
[tex]\displaystyle x=\frac{-2\pm 2\sqrt{7}}{2}=-1 \pm \sqrt{7}[/tex]
