Solve (x)^(3)-(K-1)(x)^(2)+Kx+54=0 | 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

$${ x }^{ 3 } -(K-1) { x }^{ 2 } +Kx+54=0$$

Solve for K

$K=-\frac{x^{3}+x^{2}+54}{x\left(1-x\right)}$
$x\neq 1\text{ and }x\neq 0$

Steps for Solving Linear Equation

Use the distributive property to multiply $K-1$ by $x^{2}$.

$$x^{3}-\left(Kx^{2}-x^{2}\right)+Kx+54=0$$

To find the opposite of $Kx^{2}-x^{2}$, find the opposite of each term.

$$x^{3}-Kx^{2}+x^{2}+Kx+54=0$$

Subtract $x^{3}$ from both sides. Anything subtracted from zero gives its negation.

$$-Kx^{2}+x^{2}+Kx+54=-x^{3}$$

Subtract $x^{2}$ from both sides.

$$-Kx^{2}+Kx+54=-x^{3}-x^{2}$$

Subtract $54$ from both sides.

$$-Kx^{2}+Kx=-x^{3}-x^{2}-54$$

Combine all terms containing $K$.

$$\left(-x^{2}+x\right)K=-x^{3}-x^{2}-54$$

The equation is in standard form.

$$\left(x-x^{2}\right)K=-x^{3}-x^{2}-54$$

Divide both sides by $-x^{2}+x$.

$$\frac{\left(x-x^{2}\right)K}{x-x^{2}}=\frac{-x^{3}-x^{2}-54}{x-x^{2}}$$

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

$$K=\frac{-x^{3}-x^{2}-54}{x-x^{2}}$$

Divide $-x^{3}-x^{2}-54$ by $-x^{2}+x$.

$$K=-\frac{x^{3}+x^{2}+54}{x\left(1-x\right)}$$