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

$$x ( x + 2 ) - 8 = 2 x + 1$$

Solve for x

$$x=-3$$

$$x=3$$

Steps by Finding Square Root

Use the distributive property to multiply x by x+2.

$$x^{2}+2x-8=2x+1$$

Subtract 2x from both sides.

$$x^{2}+2x-8-2x=1$$

Combine 2x and -2x to get 0.

$$x^{2}-8=1$$

Add 8 to both sides.

$$x^{2}=1+8$$

Add 1 and 8 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

Use the distributive property to multiply x by x+2.

$$x^{2}+2x-8=2x+1$$

Subtract 2x from both sides.

$$x^{2}+2x-8-2x=1$$

Combine 2x and -2x to get 0.

$$x^{2}-8=1$$

Subtract 1 from both sides.

$$x^{2}-8-1=0$$

Subtract 1 from -8 to get -9.

$$x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)}}{2}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36}}{2}$$

Take the square root of 36.

$$x=\frac{0±6}{2}$$

Now solve the equation x=\frac{0±6}{2} when ± is plus. Divide 6 by 2.

$$x=3$$

Now solve the equation x=\frac{0±6}{2} when ± is minus. Divide -6 by 2.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$