Solve for d
d\in \mathrm{C}
x=-\sqrt{2}i+1\text{ or }x=1+\sqrt{2}i\text{ or }x=0
Solve for a
a\in \mathrm{C}
x=-\sqrt{2}i+1\text{ or }x=1+\sqrt{2}i\text{ or }x=0
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x=x^{3}-2x^{2}+4x-5ma^{2}knilaidari\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2
Multiply a and a to get a^{2}.
x=x^{3}-2x^{2}+4x-5ma^{3}knilidari\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x=x^{3}-2x^{2}+4x-5ma^{4}knilidri\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
x=x^{3}-2x^{2}+4x-5ima^{4}knlidri\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2
Multiply 5 and i to get 5i.
x=x^{3}-2x^{2}+4x-\left(-5ma^{4}knldri\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2\right)
Multiply 5i and i to get -5.
x=x^{3}-2x^{2}+4x-\left(-5ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)\times 2\right)
Multiply -5 and i to get -5i.
x=x^{3}-2x^{2}+4x-\left(-10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)\right)
Multiply -5i and 2 to get -10i.
x^{3}-2x^{2}+4x-\left(-10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)\right)=x
Swap sides so that all variable terms are on the left hand side.
x^{3}-2x^{2}+4x+10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)=x
Multiply -1 and -10i to get 10i.
-2x^{2}+4x+10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)=x-x^{3}
Subtract x^{3} from both sides.
4x+10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)=x-x^{3}+2x^{2}
Add 2x^{2} to both sides.
10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)=x-x^{3}+2x^{2}-4x
Subtract 4x from both sides.
10ima^{4}knldr\frac{\mathrm{d}}{\mathrm{d}x}(f)=-3x-x^{3}+2x^{2}
Combine x and -4x to get -3x.
0=-x^{3}+2x^{2}-3x
The equation is in standard form.
d\in
This is false for any d.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}