Solve 2^2-(x-3)(x+3)=2

$$2 ^ { 2 } - ( x - 3 ) ( x + 3 ) = 2$$

Solve for x

$$x=\sqrt{11}\approx 3.31662479$$

$$x=-\sqrt{11}\approx -3.31662479$$

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$4-\left(x-3\right)\left(x+3\right)=2$$

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.

$$4-\left(x^{2}-9\right)=2$$

To find the opposite of x^{2}-9, find the opposite of each term.

$$4-x^{2}+9=2$$

Add 4 and 9 to get 13.

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

Subtract 13 from both sides.

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

Subtract 13 from 2 to get -11.

$$-x^{2}=-11$$

Divide both sides by -1.

$$x^{2}=\frac{-11}{-1}$$

Fraction \frac{-11}{-1} can be simplified to 11 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=11$$

Take the square root of both sides of the equation.

$$x=\sqrt{11} x=-\sqrt{11}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$4-\left(x-3\right)\left(x+3\right)=2$$

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.

$$4-\left(x^{2}-9\right)=2$$

To find the opposite of x^{2}-9, find the opposite of each term.

$$4-x^{2}+9=2$$

Add 4 and 9 to get 13.

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

Subtract 2 from both sides.

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

Subtract 2 from 13 to get 11.

$$11-x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-x^{2}+11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 11}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 11}}{2\left(-1\right)}$$

Multiply 4 times 11.

$$x=\frac{0±\sqrt{44}}{2\left(-1\right)}$$

Take the square root of 44.

$$x=\frac{0±2\sqrt{11}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{11}}{-2}$$

Now solve the equation x=\frac{0±2\sqrt{11}}{-2} when ± is plus.

$$x=-\sqrt{11}$$

Now solve the equation x=\frac{0±2\sqrt{11}}{-2} when ± is minus.

$$x=\sqrt{11}$$

The equation is now solved.

$$x=-\sqrt{11} x=\sqrt{11}$$