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

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

Solve for x

$$x=-3$$

$$x=3$$

Steps by Finding Square Root

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.

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

Add 1 to both sides.

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

Add 8 and 1 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

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.

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

Subtract 8 from both sides.

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

Subtract 8 from -1 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.

$$x=3 x=-3$$