Solve 3CO(S)^(-1)x+SI(N)^(-1)x= pi | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3CO { S }^{ -1 } x+SI { N }^{ -1 } x= \pi$$

Solve for C (complex solution)

$\left\{\begin{matrix}C=-\frac{S\left(ISx-\pi N\right)}{3NOx}\text{, }&N\neq 0\text{ and }O\neq 0\text{ and }x\neq 0\text{ and }S\neq 0\\C\in \mathrm{C}\text{, }&S=\frac{\pi N}{Ix}\text{ and }I\neq 0\text{ and }x\neq 0\text{ and }O=0\text{ and }N\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Subtract $SIN^{-1}x$ from both sides.

$$3COS^{-1}x=\pi -SIN^{-1}x$$

Reorder the terms.

$$3\times \frac{1}{S}COx=\pi -\frac{1}{N}ISx$$

Multiply both sides of the equation by $NS$, the least common multiple of $S,N$.

$$3N\times 1COx=NS\pi -\frac{1}{N}ISxNS$$

Multiply $3$ and $1$ to get $3$.

$$3NCOx=NS\pi -\frac{1}{N}ISxNS$$

Multiply $S$ and $S$ to get $S^{2}$.

$$3NCOx=NS\pi -\frac{1}{N}IS^{2}xN$$

Express $\frac{1}{N}I$ as a single fraction.

$$3NCOx=NS\pi -\frac{I}{N}S^{2}xN$$

Express $\frac{I}{N}S^{2}$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}}{N}xN$$

Express $\frac{IS^{2}}{N}x$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}x}{N}N$$

Express $\frac{IS^{2}x}{N}N$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}xN}{N}$$

Cancel out $N$ in both numerator and denominator.

$$3NCOx=NS\pi -IxS^{2}$$

The equation is in standard form.

$$3NOxC=\pi NS-IxS^{2}$$

Divide both sides by $3NOx$.

$$\frac{3NOxC}{3NOx}=\frac{S\left(\pi N-ISx\right)}{3NOx}$$

Dividing by $3NOx$ undoes the multiplication by $3NOx$.

$$C=\frac{S\left(\pi N-ISx\right)}{3NOx}$$

Solve for C

$\left\{\begin{matrix}C=-\frac{S\left(ISx-\pi N\right)}{3NOx}\text{, }&N\neq 0\text{ and }O\neq 0\text{ and }x\neq 0\text{ and }S\neq 0\\C\in \mathrm{R}\text{, }&S=\frac{\pi N}{Ix}\text{ and }I\neq 0\text{ and }x\neq 0\text{ and }O=0\text{ and }N\neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Subtract $SIN^{-1}x$ from both sides.

$$3COS^{-1}x=\pi -SIN^{-1}x$$

Reorder the terms.

$$3\times \frac{1}{S}COx=\pi -\frac{1}{N}ISx$$

Multiply both sides of the equation by $NS$, the least common multiple of $S,N$.

$$3N\times 1COx=NS\pi -\frac{1}{N}ISxNS$$

Multiply $3$ and $1$ to get $3$.

$$3NCOx=NS\pi -\frac{1}{N}ISxNS$$

Multiply $S$ and $S$ to get $S^{2}$.

$$3NCOx=NS\pi -\frac{1}{N}IS^{2}xN$$

Express $\frac{1}{N}I$ as a single fraction.

$$3NCOx=NS\pi -\frac{I}{N}S^{2}xN$$

Express $\frac{I}{N}S^{2}$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}}{N}xN$$

Express $\frac{IS^{2}}{N}x$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}x}{N}N$$

Express $\frac{IS^{2}x}{N}N$ as a single fraction.

$$3NCOx=NS\pi -\frac{IS^{2}xN}{N}$$

Cancel out $N$ in both numerator and denominator.

$$3NCOx=NS\pi -IxS^{2}$$

The equation is in standard form.

$$3NOxC=\pi NS-IxS^{2}$$

Divide both sides by $3NOx$.

$$\frac{3NOxC}{3NOx}=\frac{S\left(\pi N-ISx\right)}{3NOx}$$

Dividing by $3NOx$ undoes the multiplication by $3NOx$.

$$C=\frac{S\left(\pi N-ISx\right)}{3NOx}$$

Solve for I

$I=\frac{N\left(\pi S-3COx\right)}{xS^{2}}$
$S\neq 0\text{ and }x\neq 0\text{ and }N\neq 0$

Steps for Solving Linear Equation

Subtract $3COS^{-1}x$ from both sides.

$$SIN^{-1}x=\pi -3COS^{-1}x$$

Reorder the terms.

$$\frac{1}{N}ISx=\pi -3\times \frac{1}{S}COx$$

Multiply both sides of the equation by $NS$, the least common multiple of $N,S$.

$$S\times 1ISx=NS\pi -3\times \frac{1}{S}COxNS$$

Multiply $S$ and $S$ to get $S^{2}$.

$$S^{2}\times 1Ix=NS\pi -3\times \frac{1}{S}COxNS$$

Express $-3\times \frac{1}{S}$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3}{S}COxNS$$

Express $\frac{-3}{S}C$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3C}{S}OxNS$$

Express $\frac{-3C}{S}O$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3CO}{S}xNS$$

Express $\frac{-3CO}{S}x$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3COx}{S}NS$$

Express $\frac{-3COx}{S}N$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3COxN}{S}S$$

Express $\frac{-3COxN}{S}S$ as a single fraction.

$$S^{2}\times 1Ix=NS\pi +\frac{-3COxNS}{S}$$

Cancel out $S$ in both numerator and denominator.

$$S^{2}\times 1Ix=NS\pi -3CNOx$$

Reorder the terms.

$$IxS^{2}=-3CNOx+\pi NS$$

The equation is in standard form.

$$xS^{2}I=\pi NS-3CNOx$$

Divide both sides by $xS^{2}$.

$$\frac{xS^{2}I}{xS^{2}}=\frac{N\left(\pi S-3COx\right)}{xS^{2}}$$

Dividing by $xS^{2}$ undoes the multiplication by $xS^{2}$.

$$I=\frac{N\left(\pi S-3COx\right)}{xS^{2}}$$