Solve (sqrt{11}-x)(sqrt{11}+x)=11

$$( \sqrt { 11 } - x ) ( \sqrt { 11 } + x ) = 11$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Consider \left(\sqrt{11}-x\right)\left(\sqrt{11}+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{11}\right)^{2}-x^{2}=11$$

The square of \sqrt{11} is 11.

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

Subtract 11 from both sides.

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

Subtract 11 from 11 to get 0.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Consider \left(\sqrt{11}-x\right)\left(\sqrt{11}+x\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{11}\right)^{2}-x^{2}=11$$

The square of \sqrt{11} is 11.

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

Subtract 11 from both sides.

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

Subtract 11 from 11 to get 0.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$