Solve (x+1)(2x+8)=(x+7)(x+3)

$$( x + 1 ) ( 2 x + 8 ) = ( x + 7 ) ( x + 3 )$$

Solve for x

$$x=\sqrt{13}\approx 3.605551275$$

$$x=-\sqrt{13}\approx -3.605551275$$

Steps by Finding Square Root

Use the distributive property to multiply x+1 by 2x+8 and combine like terms.

$$2x^{2}+10x+8=\left(x+7\right)\left(x+3\right)$$

Use the distributive property to multiply x+7 by x+3 and combine like terms.

$$2x^{2}+10x+8=x^{2}+10x+21$$

Subtract x^{2} from both sides.

$$2x^{2}+10x+8-x^{2}=10x+21$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+10x+8=10x+21$$

Subtract 10x from both sides.

$$x^{2}+10x+8-10x=21$$

Combine 10x and -10x to get 0.

$$x^{2}+8=21$$

Subtract 8 from both sides.

$$x^{2}=21-8$$

Subtract 8 from 21 to get 13.

$$x^{2}=13$$

Take the square root of both sides of the equation.

$$x=\sqrt{13} x=-\sqrt{13}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by 2x+8 and combine like terms.

$$2x^{2}+10x+8=\left(x+7\right)\left(x+3\right)$$

Use the distributive property to multiply x+7 by x+3 and combine like terms.

$$2x^{2}+10x+8=x^{2}+10x+21$$

Subtract x^{2} from both sides.

$$2x^{2}+10x+8-x^{2}=10x+21$$

Combine 2x^{2} and -x^{2} to get x^{2}.

$$x^{2}+10x+8=10x+21$$

Subtract 10x from both sides.

$$x^{2}+10x+8-10x=21$$

Combine 10x and -10x to get 0.

$$x^{2}+8=21$$

Subtract 21 from both sides.

$$x^{2}+8-21=0$$

Subtract 21 from 8 to get -13.

$$x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-13\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-13\right)}}{2}$$

Multiply -4 times -13.

$$x=\frac{0±\sqrt{52}}{2}$$

Take the square root of 52.

$$x=\frac{0±2\sqrt{13}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{2} when ± is plus.

$$x=\sqrt{13}$$

Now solve the equation x=\frac{0±2\sqrt{13}}{2} when ± is minus.

$$x=-\sqrt{13}$$

The equation is now solved.

$$x=\sqrt{13} x=-\sqrt{13}$$