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Solve for x (complex solution)
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t^{2}-t-6=0
Substitute t for x^{2}.
t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-6\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -1 for b, and -6 for c in the quadratic formula.
t=\frac{1±5}{2}
Do the calculations.
t=3 t=-2
Solve the equation t=\frac{1±5}{2} when ± is plus and when ± is minus.
x=-\sqrt{3} x=\sqrt{3} x=-\sqrt{2}i x=\sqrt{2}i
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
t^{2}-t-6=0
Substitute t for x^{2}.
t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-6\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -1 for b, and -6 for c in the quadratic formula.
t=\frac{1±5}{2}
Do the calculations.
t=3 t=-2
Solve the equation t=\frac{1±5}{2} when ± is plus and when ± is minus.
x=\sqrt{3} x=-\sqrt{3}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.