Solve x+(x+2)/2*(x-1)=8

$$\frac { x + ( x + 2 ) } { 2 } \cdot ( x - 1 ) = 8$$

Solve for x

$$x=-3$$

$$x=3$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$\left(x+x+2\right)\left(x-1\right)=16$$

Combine x and x to get 2x.

$$\left(2x+2\right)\left(x-1\right)=16$$

Apply the distributive property by multiplying each term of 2x+2 by each term of x-1.

$$2x^{2}-2x+2x-2=16$$

Combine -2x and 2x to get 0.

$$2x^{2}-2=16$$

Add 2 to both sides.

$$2x^{2}=16+2$$

Add 16 and 2 to get 18.

$$2x^{2}=18$$

Divide both sides by 2.

$$x^{2}=\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$\left(x+x+2\right)\left(x-1\right)=16$$

Combine x and x to get 2x.

$$\left(2x+2\right)\left(x-1\right)=16$$

Apply the distributive property by multiplying each term of 2x+2 by each term of x-1.

$$2x^{2}-2x+2x-2=16$$

Combine -2x and 2x to get 0.

$$2x^{2}-2=16$$

Subtract 16 from both sides.

$$2x^{2}-2-16=0$$

Subtract 16 from -2 to get -18.

$$2x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Multiply -8 times -18.

$$x=\frac{0±\sqrt{144}}{2\times 2}$$

Take the square root of 144.

$$x=\frac{0±12}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±12}{4}$$

Now solve the equation x=\frac{0±12}{4} when ± is plus. Divide 12 by 4.

$$x=3$$

Now solve the equation x=\frac{0±12}{4} when ± is minus. Divide -12 by 4.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$