Solve for x (complex solution)
x=-\frac{9^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(-\sqrt{3}\sqrt[3]{\sqrt{354}-27}i-\sqrt[3]{\sqrt{354}-27}+2\sqrt[3]{-\sqrt{354}-27}\right)}{36}\approx -0.108741282-1.4897681i
x=\frac{9^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{354}-27}+\sqrt[3]{-\sqrt{354}-27}\right)}{9}\approx 1.344547662+2.328824863i
x=-\frac{9^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(-\sqrt[3]{\sqrt{354}-27}+2\sqrt[3]{-\sqrt{354}-27}+\sqrt{3}\sqrt[3]{\sqrt{354}-27}i\right)}{36}\approx -1.23580638-0.839056763i
Solve for x
x = -\frac{9 ^ {\frac{2}{3}} {(\sqrt[3]{\sqrt{354} + 27} + \sqrt[3]{27 - \sqrt{354}})}}{9} \approx -2.689095324
Graph
Share
Copied to clipboard
x^{2}x^{2}-5x^{2}+6x=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
x^{4}-5x^{2}+6x=0
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
t^{2}-5t+6=0
Substitute t for x^{2}.
t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\times 6}}{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, -5 for b, and 6 for c in the quadratic formula.
t=\frac{5±1}{2}
Do the calculations.
t=3 t=2
Solve the equation t=\frac{5±1}{2} when ± is plus and when ± is minus.
x=-\sqrt{3} x=\sqrt{3} x=-\sqrt{2} x=\sqrt{2}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
x^{2}x^{2}-5x^{2}+6x=0
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{2}.
x^{4}-5x^{2}+6x=0
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
t^{2}-5t+6=0
Substitute t for x^{2}.
t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\times 6}}{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, -5 for b, and 6 for c in the quadratic formula.
t=\frac{5±1}{2}
Do the calculations.
t=3 t=2
Solve the equation t=\frac{5±1}{2} when ± is plus and when ± is minus.
x=\sqrt{3} x=-\sqrt{3} x=\sqrt{2} x=-\sqrt{2}
Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}