Solve (x+1)(x-1)/2=21

$$\frac{ (x+1)(x-1) }{ 2 } =21$$

Solve for x

$$x=\sqrt{43}\approx 6.557438524$$

$$x=-\sqrt{43}\approx -6.557438524$$

Steps by Finding Square Root

Multiply both sides by 2.

$$\left(x+1\right)\left(x-1\right)=21\times 2$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}-1=21\times 2$$

Multiply 21 and 2 to get 42.

$$x^{2}-1=42$$

Add 1 to both sides.

$$x^{2}=42+1$$

Add 42 and 1 to get 43.

$$x^{2}=43$$

Take the square root of both sides of the equation.

$$x=\sqrt{43} x=-\sqrt{43}$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$\left(x+1\right)\left(x-1\right)=21\times 2$$

Consider \left(x+1\right)\left(x-1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}-1=21\times 2$$

Multiply 21 and 2 to get 42.

$$x^{2}-1=42$$

Subtract 42 from both sides.

$$x^{2}-1-42=0$$

Subtract 42 from -1 to get -43.

$$x^{2}-43=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -43 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-43\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-43\right)}}{2}$$

Multiply -4 times -43.

$$x=\frac{0±\sqrt{172}}{2}$$

Take the square root of 172.

$$x=\frac{0±2\sqrt{43}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{43}}{2} when ± is plus.

$$x=\sqrt{43}$$

Now solve the equation x=\frac{0±2\sqrt{43}}{2} when ± is minus.

$$x=-\sqrt{43}$$

The equation is now solved.

$$x=\sqrt{43} x=-\sqrt{43}$$