Solve p(x) * 2x ^ 2 + 6x + 1 = 31w | 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

$$p(x)\cdot2x^{2}+6x+1=31\ w$$

Solve for p (complex solution)

$\left\{\begin{matrix}p=-\frac{6x-31w+1}{2x^{3}}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&x=0\text{ and }w=\frac{1}{31}\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$px^{3}\times 2+6x+1=31w$$

Subtract $6x$ from both sides.

$$px^{3}\times 2+1=31w-6x$$

Subtract $1$ from both sides.

$$px^{3}\times 2=31w-6x-1$$

The equation is in standard form.

$$2x^{3}p=-6x+31w-1$$

Divide both sides by $2x^{3}$.

$$\frac{2x^{3}p}{2x^{3}}=\frac{-6x+31w-1}{2x^{3}}$$

Dividing by $2x^{3}$ undoes the multiplication by $2x^{3}$.

$$p=\frac{-6x+31w-1}{2x^{3}}$$

Solve for p

$\left\{\begin{matrix}p=-\frac{6x-31w+1}{2x^{3}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }w=\frac{1}{31}\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$px^{3}\times 2+6x+1=31w$$

Subtract $6x$ from both sides.

$$px^{3}\times 2+1=31w-6x$$

Subtract $1$ from both sides.

$$px^{3}\times 2=31w-6x-1$$

The equation is in standard form.

$$2x^{3}p=-6x+31w-1$$

Divide both sides by $2x^{3}$.

$$\frac{2x^{3}p}{2x^{3}}=\frac{-6x+31w-1}{2x^{3}}$$

Dividing by $2x^{3}$ undoes the multiplication by $2x^{3}$.

$$p=\frac{-6x+31w-1}{2x^{3}}$$

Solve for w

$w=\frac{2px^{3}+6x+1}{31}$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$px^{3}\times 2+6x+1=31w$$

Swap sides so that all variable terms are on the left hand side.

$$31w=px^{3}\times 2+6x+1$$

The equation is in standard form.

$$31w=2px^{3}+6x+1$$

Divide both sides by $31$.

$$\frac{31w}{31}=\frac{2px^{3}+6x+1}{31}$$

Dividing by $31$ undoes the multiplication by $31$.

$$w=\frac{2px^{3}+6x+1}{31}$$