Solve for x (complex solution)



Solve for x

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t^{2}-8t-4=0
Substitute t for x^{2}.
t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-4\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, -8 for b, and -4 for c in the quadratic formula.
t=\frac{8±4\sqrt{5}}{2}
Do the calculations.
t=2\sqrt{5}+4 t=4-2\sqrt{5}
Solve the equation t=\frac{8±4\sqrt{5}}{2} when ± is plus and when ± is minus.
x=-\sqrt{2\sqrt{5}+4} x=\sqrt{2\sqrt{5}+4} x=-i\sqrt{-\left(4-2\sqrt{5}\right)} x=i\sqrt{-\left(4-2\sqrt{5}\right)}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
t^{2}-8t-4=0
Substitute t for x^{2}.
t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-4\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, -8 for b, and -4 for c in the quadratic formula.
t=\frac{8±4\sqrt{5}}{2}
Do the calculations.
t=2\sqrt{5}+4 t=4-2\sqrt{5}
Solve the equation t=\frac{8±4\sqrt{5}}{2} when ± is plus and when ± is minus.
x=\frac{\sqrt{8\sqrt{5}+16}}{2} x=-\frac{\sqrt{8\sqrt{5}+16}}{2}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.