Solve Sigma(x-45)^2=3089

$$\Sigma ( x - 45 ) ^ { 2 } = 3089$$

Solve for Σ

$$Σ=\frac{3089}{\left(x-45\right)^{2}}$$

$$x\neq 45$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-45\right)^{2}.

$$Σ\left(x^{2}-90x+2025\right)=3089$$

Use the distributive property to multiply Σ by x^{2}-90x+2025.

$$Σx^{2}-90Σx+2025Σ=3089$$

Combine all terms containing Σ.

$$\left(x^{2}-90x+2025\right)Σ=3089$$

Divide both sides by x^{2}-90x+2025.

$$\frac{\left(x^{2}-90x+2025\right)Σ}{x^{2}-90x+2025}=\frac{3089}{x^{2}-90x+2025}$$

Dividing by x^{2}-90x+2025 undoes the multiplication by x^{2}-90x+2025.

$$Σ=\frac{3089}{x^{2}-90x+2025}$$

Divide 3089 by x^{2}-90x+2025.

$$Σ=\frac{3089}{\left(x-45\right)^{2}}$$

Solve for x (complex solution)

$$x=45+\sqrt{3089}Σ^{-\frac{1}{2}}$$

$$x=45-\sqrt{3089}Σ^{-\frac{1}{2}}\text{, }Σ\neq 0$$

Solve for x

$$x=45+\sqrt{\frac{3089}{Σ}}$$

$$x=45-\sqrt{\frac{3089}{Σ}}\text{, }Σ>0$$