Solve (x-2)^2-(x-3)(x+3)=2x+4

$$( x - 2 ) ^ { 2 } - ( x - 3 ) ( x + 3 ) = 2 x + 4$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.

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

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.

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

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

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

Combine x^{2} and -x^{2} to get 0.

$$-4x+4+9=2x+4$$

Add 4 and 9 to get 13.

$$-4x+13=2x+4$$

Subtract 2x from both sides.

$$-4x+13-2x=4$$

Combine -4x and -2x to get -6x.

$$-6x+13=4$$

Subtract 13 from both sides.

$$-6x=4-13$$

Subtract 13 from 4 to get -9.

$$-6x=-9$$

Divide both sides by -6.

$$x=\frac{-9}{-6}$$

Reduce the fraction \frac{-9}{-6} to lowest terms by extracting and canceling out -3.

$$x=\frac{3}{2}$$