Solve 9x^2-36=0

$$9 { x }^{ 2 } -36=0$$

Solve for x

$$x=2$$

$$x=-2$$

Steps Using Difference of Squares

Divide both sides by 9.

$$x^{2}-4=0$$

Consider x^{2}-4. Rewrite x^{2}-4 as x^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-2\right)\left(x+2\right)=0$$

To find equation solutions, solve x-2=0 and x+2=0.

$$x=2 x=-2$$

Steps by Finding Square Root

Add 36 to both sides. Anything plus zero gives itself.

$$9x^{2}=36$$

Divide both sides by 9.

$$x^{2}=\frac{36}{9}$$

Divide 36 by 9 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$9x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-36\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-36\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-36\right)}}{2\times 9}$$

Multiply -36 times -36.

$$x=\frac{0±\sqrt{1296}}{2\times 9}$$

Take the square root of 1296.

$$x=\frac{0±36}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±36}{18}$$

Now solve the equation x=\frac{0±36}{18} when ± is plus. Divide 36 by 18.

$$x=2$$

Now solve the equation x=\frac{0±36}{18} when ± is minus. Divide -36 by 18.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$