Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{x}{4}+\frac{a}{2c}\text{, }&c\neq 0\\b\in \mathrm{C}\text{, }&a=0\text{ and }c=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{x}{4}+\frac{a}{2c}\text{, }&c\neq 0\\b\in \mathrm{R}\text{, }&a=0\text{ and }c=0\end{matrix}\right.
Solve for a
a=-\frac{c\left(x-4b\right)}{2}
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a=\left(2b+2\left(-\frac{x}{4}\right)\right)c
Use the distributive property to multiply b-\frac{x}{4} by 2.
a=\left(2b+\frac{x}{-2}\right)c
Cancel out 4, the greatest common factor in 2 and 4.
a=2bc+\frac{x}{-2}c
Use the distributive property to multiply 2b+\frac{x}{-2} by c.
a=2bc+\frac{xc}{-2}
Express \frac{x}{-2}c as a single fraction.
2bc+\frac{xc}{-2}=a
Swap sides so that all variable terms are on the left hand side.
2bc=a-\frac{xc}{-2}
Subtract \frac{xc}{-2} from both sides.
-4bc=-2a-xc
Multiply both sides of the equation by -2.
-4bc=-cx-2a
Reorder the terms.
\left(-4c\right)b=-cx-2a
The equation is in standard form.
\frac{\left(-4c\right)b}{-4c}=\frac{-cx-2a}{-4c}
Divide both sides by -4c.
b=\frac{-cx-2a}{-4c}
Dividing by -4c undoes the multiplication by -4c.
b=\frac{x}{4}+\frac{a}{2c}
Divide -2a-cx by -4c.
a=\left(2b+2\left(-\frac{x}{4}\right)\right)c
Use the distributive property to multiply b-\frac{x}{4} by 2.
a=\left(2b+\frac{x}{-2}\right)c
Cancel out 4, the greatest common factor in 2 and 4.
a=2bc+\frac{x}{-2}c
Use the distributive property to multiply 2b+\frac{x}{-2} by c.
a=2bc+\frac{xc}{-2}
Express \frac{x}{-2}c as a single fraction.
2bc+\frac{xc}{-2}=a
Swap sides so that all variable terms are on the left hand side.
2bc=a-\frac{xc}{-2}
Subtract \frac{xc}{-2} from both sides.
-4bc=-2a-xc
Multiply both sides of the equation by -2.
-4bc=-cx-2a
Reorder the terms.
\left(-4c\right)b=-cx-2a
The equation is in standard form.
\frac{\left(-4c\right)b}{-4c}=\frac{-cx-2a}{-4c}
Divide both sides by -4c.
b=\frac{-cx-2a}{-4c}
Dividing by -4c undoes the multiplication by -4c.
b=\frac{x}{4}+\frac{a}{2c}
Divide -2a-cx by -4c.
Examples
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{ 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}