Solve (x-2)^2-(x+3)(x-3)=4x-1

$$( x - 2 ) ^ { 2 } - ( x + 3 ) ( x - 3 ) = 4 x - 1$$

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}.

$$x^{2}-4x+4-\left(x+3\right)\left(x-3\right)=4x-1$$

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.

$$x^{2}-4x+4-\left(x^{2}-9\right)=4x-1$$

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

$$x^{2}-4x+4-x^{2}+9=4x-1$$

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

$$-4x+4+9=4x-1$$

Add 4 and 9 to get 13.

$$-4x+13=4x-1$$

Subtract 4x from both sides.

$$-4x+13-4x=-1$$

Combine -4x and -4x to get -8x.

$$-8x+13=-1$$

Subtract 13 from both sides.

$$-8x=-1-13$$

Subtract 13 from -1 to get -14.

$$-8x=-14$$

Divide both sides by -8.

$$x=\frac{-14}{-8}$$

Reduce the fraction \frac{-14}{-8} to lowest terms by extracting and canceling out -2.

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