Solve 3x^2-768=0

$$3 x ^ { 2 } - 768 = 0$$

Solve for x

$$x=16$$

$$x=-16$$

Steps Using Difference of Squares

Divide both sides by 3.

$$x^{2}-256=0$$

Consider x^{2}-256. Rewrite x^{2}-256 as x^{2}-16^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-16\right)\left(x+16\right)=0$$

To find equation solutions, solve x-16=0 and x+16=0.

$$x=16 x=-16$$

Steps by Finding Square Root

Add 768 to both sides. Anything plus zero gives itself.

$$3x^{2}=768$$

Divide both sides by 3.

$$x^{2}=\frac{768}{3}$$

Divide 768 by 3 to get 256.

$$x^{2}=256$$

Take the square root of both sides of the equation.

$$x=16 x=-16$$

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.

$$3x^{2}-768=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -768 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-768\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-768\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-768\right)}}{2\times 3}$$

Multiply -12 times -768.

$$x=\frac{0±\sqrt{9216}}{2\times 3}$$

Take the square root of 9216.

$$x=\frac{0±96}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±96}{6}$$

Now solve the equation x=\frac{0±96}{6} when ± is plus. Divide 96 by 6.

$$x=16$$

Now solve the equation x=\frac{0±96}{6} when ± is minus. Divide -96 by 6.

$$x=-16$$

The equation is now solved.

$$x=16 x=-16$$