Solve 2w^2-8=0

$$2 w ^ { 2 } - 8 = 0$$

Solve for w

$$w=2$$

$$w=-2$$

Steps Using Difference of Squares

Divide both sides by 2.

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

Consider w^{2}-4. Rewrite w^{2}-4 as w^{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).

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

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

$$w=2 w=-2$$

Steps by Finding Square Root

Add 8 to both sides. Anything plus zero gives itself.

$$2w^{2}=8$$

Divide both sides by 2.

$$w^{2}=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$w^{2}=4$$

Take the square root of both sides of the equation.

$$w=2 w=-2$$

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.

$$2w^{2}-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 2\left(-8\right)}}{2\times 2}$$

Multiply -4 times 2.

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

Multiply -8 times -8.

$$w=\frac{0±\sqrt{64}}{2\times 2}$$

Take the square root of 64.

$$w=\frac{0±8}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{0±8}{4}$$

Now solve the equation w=\frac{0±8}{4} when ± is plus. Divide 8 by 4.

$$w=2$$

Now solve the equation w=\frac{0±8}{4} when ± is minus. Divide -8 by 4.

$$w=-2$$

The equation is now solved.

$$w=2 w=-2$$