Solve x^2-25=(x-5)(x+5)

$$x ^ { 2 } - 25 = ( x - 5 ) ( x + 5 )$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Consider \left(x-5\right)\left(x+5\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 5.

$$x^{2}-25=x^{2}-25$$

Subtract x^{2} from both sides.

$$x^{2}-25-x^{2}=-25$$

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

$$-25=-25$$

Compare -25 and -25.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Consider \left(x-5\right)\left(x+5\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 5.

$$x^{2}-25=x^{2}-25$$

Subtract x^{2} from both sides.

$$x^{2}-25-x^{2}=-25$$

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

$$-25=-25$$

Compare -25 and -25.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$