Solve (x+2)^3/120+2(10x5)*4=130

$$\frac { ( x + 2 ) ^ { 3 } } { 120 } + 2 ( 10 x 5 ) \times 4 = 130$$

Solve for x_5

$$x_{5}=-\frac{\left(x+2\right)^{3}}{9600}+\frac{13}{8}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120.

$$\left(x+2\right)^{3}+240\times 10x_{5}\times 4=15600$$

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$x^{3}+6x^{2}+12x+8+240\times 10x_{5}\times 4=15600$$

Multiply 240 and 10 to get 2400.

$$x^{3}+6x^{2}+12x+8+2400x_{5}\times 4=15600$$

Multiply 2400 and 4 to get 9600.

$$x^{3}+6x^{2}+12x+8+9600x_{5}=15600$$

Subtract x^{3} from both sides.

$$6x^{2}+12x+8+9600x_{5}=15600-x^{3}$$

Subtract 6x^{2} from both sides.

$$12x+8+9600x_{5}=15600-x^{3}-6x^{2}$$

Subtract 12x from both sides.

$$8+9600x_{5}=15600-x^{3}-6x^{2}-12x$$

Subtract 8 from both sides.

$$9600x_{5}=15600-x^{3}-6x^{2}-12x-8$$

Subtract 8 from 15600 to get 15592.

$$9600x_{5}=15592-x^{3}-6x^{2}-12x$$

The equation is in standard form.

$$9600x_{5}=15592-12x-6x^{2}-x^{3}$$

Divide both sides by 9600.

$$\frac{9600x_{5}}{9600}=\frac{15592-12x-6x^{2}-x^{3}}{9600}$$

Dividing by 9600 undoes the multiplication by 9600.

$$x_{5}=\frac{15592-12x-6x^{2}-x^{3}}{9600}$$

Divide 15592-x^{3}-6x^{2}-12x by 9600.

$$x_{5}=-\frac{x^{3}}{9600}-\frac{x^{2}}{1600}-\frac{x}{800}+\frac{1949}{1200}$$

Solve for x (complex solution)

$$x=2\sqrt[3]{1950-1200x_{5}}-2$$

$$x=2e^{\frac{4i\pi }{3}}\sqrt[3]{1950-1200x_{5}}-2$$

$$x=2e^{\frac{2i\pi }{3}}\sqrt[3]{1950-1200x_{5}}-2$$

Solve for x

$$x=2\sqrt[3]{1950-1200x_{5}}-2$$