Solve 115=(x+9)(x-9)

$$115 = ( x + 9 ) ( x - 9 )$$

Solve for x

$$x=14$$

$$x=-14$$

Steps by Finding Square Root

Consider \left(x+9\right)\left(x-9\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 9.

$$115=x^{2}-81$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-81=115$$

Add 81 to both sides.

$$x^{2}=115+81$$

Add 115 and 81 to get 196.

$$x^{2}=196$$

Take the square root of both sides of the equation.

$$x=14 x=-14$$

Steps Using the Quadratic Formula

Consider \left(x+9\right)\left(x-9\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 9.

$$115=x^{2}-81$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}-81=115$$

Subtract 115 from both sides.

$$x^{2}-81-115=0$$

Subtract 115 from -81 to get -196.

$$x^{2}-196=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -196 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-196\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-196\right)}}{2}$$

Multiply -4 times -196.

$$x=\frac{0±\sqrt{784}}{2}$$

Take the square root of 784.

$$x=\frac{0±28}{2}$$

Now solve the equation x=\frac{0±28}{2} when ± is plus. Divide 28 by 2.

$$x=14$$

Now solve the equation x=\frac{0±28}{2} when ± is minus. Divide -28 by 2.

$$x=-14$$

The equation is now solved.

$$x=14 x=-14$$