Solve for a
a=\frac{\sqrt{2}}{2}\approx 0.707106781
a=-\frac{\sqrt{2}}{2}\approx -0.707106781
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a=\frac{\sqrt{2}}{2} a=-\frac{\sqrt{2}}{2}
Take the square root of both sides of the equation.
a^{2}-\frac{1}{2}=0
Subtract \frac{1}{2} from both sides.
a=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{2}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
a=\frac{0±\sqrt{-4\left(-\frac{1}{2}\right)}}{2}
Square 0.
a=\frac{0±\sqrt{2}}{2}
Multiply -4 times -\frac{1}{2}.
a=\frac{\sqrt{2}}{2}
Now solve the equation a=\frac{0±\sqrt{2}}{2} when ± is plus.
a=-\frac{\sqrt{2}}{2}
Now solve the equation a=\frac{0±\sqrt{2}}{2} when ± is minus.
a=\frac{\sqrt{2}}{2} a=-\frac{\sqrt{2}}{2}
The equation is now solved.
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