Solve for z
z=2\sqrt{13}\approx 7.211102551
z=-2\sqrt{13}\approx -7.211102551
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z^{2}=2+50
Multiply z and z to get z^{2}.
z^{2}=52
Add 2 and 50 to get 52.
z=2\sqrt{13} z=-2\sqrt{13}
Take the square root of both sides of the equation.
z^{2}=2+50
Multiply z and z to get z^{2}.
z^{2}=52
Add 2 and 50 to get 52.
z^{2}-52=0
Subtract 52 from both sides.
z=\frac{0±\sqrt{0^{2}-4\left(-52\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -52 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
z=\frac{0±\sqrt{-4\left(-52\right)}}{2}
Square 0.
z=\frac{0±\sqrt{208}}{2}
Multiply -4 times -52.
z=\frac{0±4\sqrt{13}}{2}
Take the square root of 208.
z=2\sqrt{13}
Now solve the equation z=\frac{0±4\sqrt{13}}{2} when ± is plus.
z=-2\sqrt{13}
Now solve the equation z=\frac{0±4\sqrt{13}}{2} when ± is minus.
z=2\sqrt{13} z=-2\sqrt{13}
The equation is now solved.
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