Solve (q+2)(q-2)=12

$$( q + 2 ) ( q - 2 ) = 12$$

Solve for q

$$q=-4$$

$$q=4$$

Steps by Finding Square Root

Consider \left(q+2\right)\left(q-2\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 2.

$$q^{2}-4=12$$

Add 4 to both sides.

$$q^{2}=12+4$$

Add 12 and 4 to get 16.

$$q^{2}=16$$

Take the square root of both sides of the equation.

$$q=4 q=-4$$

Steps Using the Quadratic Formula

Consider \left(q+2\right)\left(q-2\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 2.

$$q^{2}-4=12$$

Subtract 12 from both sides.

$$q^{2}-4-12=0$$

Subtract 12 from -4 to get -16.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$q=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$q=\frac{0±8}{2}$$

Now solve the equation q=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$q=4$$

Now solve the equation q=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$q=-4$$

The equation is now solved.

$$q=4 q=-4$$