Solve (x+10)(x-10)=21

$$( x + 10 ) ( x - 10 ) = 21$$

Solve for x

$$x=-11$$

$$x=11$$

Steps by Finding Square Root

Consider \left(x+10\right)\left(x-10\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 10.

$$x^{2}-100=21$$

Add 100 to both sides.

$$x^{2}=21+100$$

Add 21 and 100 to get 121.

$$x^{2}=121$$

Take the square root of both sides of the equation.

$$x=11 x=-11$$

Steps Using the Quadratic Formula

Consider \left(x+10\right)\left(x-10\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 10.

$$x^{2}-100=21$$

Subtract 21 from both sides.

$$x^{2}-100-21=0$$

Subtract 21 from -100 to get -121.

$$x^{2}-121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-121\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-121\right)}}{2}$$

Multiply -4 times -121.

$$x=\frac{0±\sqrt{484}}{2}$$

Take the square root of 484.

$$x=\frac{0±22}{2}$$

Now solve the equation x=\frac{0±22}{2} when ± is plus. Divide 22 by 2.

$$x=11$$

Now solve the equation x=\frac{0±22}{2} when ± is minus. Divide -22 by 2.

$$x=-11$$

The equation is now solved.

$$x=11 x=-11$$