Solve 4x^2-324=0

$$4 x ^ { 2 } - 324 = 0$$

Solve for x

$$x=9$$

$$x=-9$$

Steps Using Difference of Squares

Divide both sides by 4.

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

Consider x^{2}-81. Rewrite x^{2}-81 as x^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

To find equation solutions, solve x-9=0 and x+9=0.

$$x=9 x=-9$$

Steps by Finding Square Root

Add 324 to both sides. Anything plus zero gives itself.

$$4x^{2}=324$$

Divide both sides by 4.

$$x^{2}=\frac{324}{4}$$

Divide 324 by 4 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

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.

$$4x^{2}-324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-324\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-324\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-324\right)}}{2\times 4}$$

Multiply -16 times -324.

$$x=\frac{0±\sqrt{5184}}{2\times 4}$$

Take the square root of 5184.

$$x=\frac{0±72}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±72}{8}$$

Now solve the equation x=\frac{0±72}{8} when ± is plus. Divide 72 by 8.

$$x=9$$

Now solve the equation x=\frac{0±72}{8} when ± is minus. Divide -72 by 8.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$