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a^{2}+4\left(\sqrt{15+3}\right)^{2}=36
Multiply both sides of the equation by 36, the least common multiple of 36,9.
a^{2}+4\left(\sqrt{18}\right)^{2}=36
Add 15 and 3 to get 18.
a^{2}+4\times 18=36
The square of \sqrt{18} is 18.
a^{2}+72=36
Multiply 4 and 18 to get 72.
a^{2}=36-72
Subtract 72 from both sides.
a^{2}=-36
Subtract 72 from 36 to get -36.
a=6i a=-6i
The equation is now solved.
a^{2}+4\left(\sqrt{15+3}\right)^{2}=36
Multiply both sides of the equation by 36, the least common multiple of 36,9.
a^{2}+4\left(\sqrt{18}\right)^{2}=36
Add 15 and 3 to get 18.
a^{2}+4\times 18=36
The square of \sqrt{18} is 18.
a^{2}+72=36
Multiply 4 and 18 to get 72.
a^{2}+72-36=0
Subtract 36 from both sides.
a^{2}+36=0
Subtract 36 from 72 to get 36.
a=\frac{0±\sqrt{0^{2}-4\times 36}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
a=\frac{0±\sqrt{-4\times 36}}{2}
Square 0.
a=\frac{0±\sqrt{-144}}{2}
Multiply -4 times 36.
a=\frac{0±12i}{2}
Take the square root of -144.
a=6i
Now solve the equation a=\frac{0±12i}{2} when ± is plus.
a=-6i
Now solve the equation a=\frac{0±12i}{2} when ± is minus.
a=6i a=-6i
The equation is now solved.