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Solve for x (complex solution)
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t^{2}-t-20=0
Substitute t for x^{2}.
t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\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 -20 for c in the quadratic formula.
t=\frac{1±9}{2}
Do the calculations.
t=5 t=-4
Solve the equation t=\frac{1±9}{2} when ± is plus and when ± is minus.
x=-\sqrt{5} x=\sqrt{5} x=-2i x=2i
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
t^{2}-t-20=0
Substitute t for x^{2}.
t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\left(-20\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 -20 for c in the quadratic formula.
t=\frac{1±9}{2}
Do the calculations.
t=5 t=-4
Solve the equation t=\frac{1±9}{2} when ± is plus and when ± is minus.
x=\sqrt{5} x=-\sqrt{5}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.