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k^{2}=18-32
Subtract 32 from both sides.
k^{2}=-14
Subtract 32 from 18 to get -14.
k=\sqrt{14}i k=-\sqrt{14}i
The equation is now solved.
32+k^{2}-18=0
Subtract 18 from both sides.
14+k^{2}=0
Subtract 18 from 32 to get 14.
k^{2}+14=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
k=\frac{0±\sqrt{0^{2}-4\times 14}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
k=\frac{0±\sqrt{-4\times 14}}{2}
Square 0.
k=\frac{0±\sqrt{-56}}{2}
Multiply -4 times 14.
k=\frac{0±2\sqrt{14}i}{2}
Take the square root of -56.
k=\sqrt{14}i
Now solve the equation k=\frac{0±2\sqrt{14}i}{2} when ± is plus.
k=-\sqrt{14}i
Now solve the equation k=\frac{0±2\sqrt{14}i}{2} when ± is minus.
k=\sqrt{14}i k=-\sqrt{14}i
The equation is now solved.