Solve c(x+1)(x+1)=27.01

$$c ( x + 1 ) ( x + 1 ) = 27.01$$

Solve for c

$$c=\frac{2701}{100\left(x+1\right)^{2}}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$c\left(x+1\right)^{2}=27.01$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$c\left(x^{2}+2x+1\right)=27.01$$

Use the distributive property to multiply c by x^{2}+2x+1.

$$cx^{2}+2cx+c=27.01$$

Combine all terms containing c.

$$\left(x^{2}+2x+1\right)c=27.01$$

Divide both sides by x^{2}+2x+1.

$$\frac{\left(x^{2}+2x+1\right)c}{x^{2}+2x+1}=\frac{27.01}{x^{2}+2x+1}$$

Dividing by x^{2}+2x+1 undoes the multiplication by x^{2}+2x+1.

$$c=\frac{27.01}{x^{2}+2x+1}$$

Divide 27.01 by x^{2}+2x+1.

$$c=\frac{2701}{100\left(x+1\right)^{2}}$$

Solve for x (complex solution)

$$x=-1+\frac{\sqrt{2701}c^{-0.5}}{10}$$

$$x=-1-\frac{\sqrt{2701}c^{-0.5}}{10}\text{, }c\neq 0$$

Solve for x

$$x=-1+\frac{\sqrt{\frac{2701}{c}}}{10}$$

$$x=-1-\frac{\sqrt{\frac{2701}{c}}}{10}\text{, }c>0$$