Solve (x+3)(x-3)=3(-1)

$$(x+3)(x-3)=3(-1)$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Consider \left(x+3\right)\left(x-3\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 3.

$$x^{2}-9=3\left(-1\right)$$

Multiply 3 and -1 to get -3.

$$x^{2}-9=-3$$

Add 9 to both sides.

$$x^{2}=-3+9$$

Add -3 and 9 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

$$x=\sqrt{6} x=-\sqrt{6}$$

Steps Using the Quadratic Formula

Consider \left(x+3\right)\left(x-3\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 3.

$$x^{2}-9=3\left(-1\right)$$

Multiply 3 and -1 to get -3.

$$x^{2}-9=-3$$

Add 3 to both sides.

$$x^{2}-9+3=0$$

Add -9 and 3 to get -6.

$$x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)}}{2}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24}}{2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2}$$

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

$$x=\sqrt{6}$$

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

$$x=-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6} x=-\sqrt{6}$$