Solve (x-2)^2-(x-3)(x+3)=6

$$( x - 2 ) ^ { 2 } - ( x - 3 ) ( x + 3 ) = 6$$

Solve for x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

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}.

$$x^{2}-4x+4-\left(x-3\right)\left(x+3\right)=6$$

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.

$$x^{2}-4x+4-\left(x^{2}-9\right)=6$$

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

$$x^{2}-4x+4-x^{2}+9=6$$

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

$$-4x+4+9=6$$

Add 4 and 9 to get 13.

$$-4x+13=6$$

Subtract 13 from both sides.

$$-4x=6-13$$

Subtract 13 from 6 to get -7.

$$-4x=-7$$

Divide both sides by -4.

$$x=\frac{-7}{-4}$$

Fraction \frac{-7}{-4} can be simplified to \frac{7}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{4}$$