Solve for x (complex solution)
x=\frac{i\sqrt{2\left(\sqrt{285}+1\right)}}{2}\approx 2.990145734i
x=-\frac{i\sqrt{2\left(\sqrt{285}+1\right)}}{2}\approx -0-2.990145734i
x = -\frac{\sqrt{2 {(\sqrt{285} - 1)}}}{2} \approx -2.817972943
x = \frac{\sqrt{2 {(\sqrt{285} - 1)}}}{2} \approx 2.817972943
Solve for x
x = -\frac{\sqrt{2 {(\sqrt{285} - 1)}}}{2} \approx -2.817972943
x = \frac{\sqrt{2 {(\sqrt{285} - 1)}}}{2} \approx 2.817972943
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x^{4}+x^{2}-71=0
Subtract 71 from both sides.
t^{2}+t-71=0
Substitute t for x^{2}.
t=\frac{-1±\sqrt{1^{2}-4\times 1\left(-71\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 -71 for c in the quadratic formula.
t=\frac{-1±\sqrt{285}}{2}
Do the calculations.
t=\frac{\sqrt{285}-1}{2} t=\frac{-\sqrt{285}-1}{2}
Solve the equation t=\frac{-1±\sqrt{285}}{2} when ± is plus and when ± is minus.
x=-\sqrt{\frac{\sqrt{285}-1}{2}} x=\sqrt{\frac{\sqrt{285}-1}{2}} x=-i\sqrt{\frac{\sqrt{285}+1}{2}} x=i\sqrt{\frac{\sqrt{285}+1}{2}}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
x^{4}+x^{2}-71=0
Subtract 71 from both sides.
t^{2}+t-71=0
Substitute t for x^{2}.
t=\frac{-1±\sqrt{1^{2}-4\times 1\left(-71\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 -71 for c in the quadratic formula.
t=\frac{-1±\sqrt{285}}{2}
Do the calculations.
t=\frac{\sqrt{285}-1}{2} t=\frac{-\sqrt{285}-1}{2}
Solve the equation t=\frac{-1±\sqrt{285}}{2} when ± is plus and when ± is minus.
x=\frac{\sqrt{2\sqrt{285}-2}}{2} x=-\frac{\sqrt{2\sqrt{285}-2}}{2}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for positive t.
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