Solve 2x^2-288=0

$$2 x ^ { 2 } - 288 = 0$$

Solve for x

$$x=12$$

$$x=-12$$

Steps Using Difference of Squares

Divide both sides by 2.

$$x^{2}-144=0$$

Consider x^{2}-144. Rewrite x^{2}-144 as x^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve x-12=0 and x+12=0.

$$x=12 x=-12$$

Steps by Finding Square Root

Add 288 to both sides. Anything plus zero gives itself.

$$2x^{2}=288$$

Divide both sides by 2.

$$x^{2}=\frac{288}{2}$$

Divide 288 by 2 to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

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.

$$2x^{2}-288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-288\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-288\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-288\right)}}{2\times 2}$$

Multiply -8 times -288.

$$x=\frac{0±\sqrt{2304}}{2\times 2}$$

Take the square root of 2304.

$$x=\frac{0±48}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±48}{4}$$

Now solve the equation x=\frac{0±48}{4} when ± is plus. Divide 48 by 4.

$$x=12$$

Now solve the equation x=\frac{0±48}{4} when ± is minus. Divide -48 by 4.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$