Solve 2w^2-18=0

$$2 { w }^{ 2 } -18=0$$

Solve for w

$$w=3$$

$$w=-3$$

Steps Using Difference of Squares

Divide both sides by 2.

$$w^{2}-9=0$$

Consider w^{2}-9. Rewrite w^{2}-9 as w^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(w-3\right)\left(w+3\right)=0$$

To find equation solutions, solve w-3=0 and w+3=0.

$$w=3 w=-3$$

Steps by Finding Square Root

Add 18 to both sides. Anything plus zero gives itself.

$$2w^{2}=18$$

Divide both sides by 2.

$$w^{2}=\frac{18}{2}$$

Divide 18 by 2 to get 9.

$$w^{2}=9$$

Take the square root of both sides of the equation.

$$w=3 w=-3$$

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.

$$2w^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Multiply -4 times 2.

$$w=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Multiply -8 times -18.

$$w=\frac{0±\sqrt{144}}{2\times 2}$$

Take the square root of 144.

$$w=\frac{0±12}{2\times 2}$$

Multiply 2 times 2.

$$w=\frac{0±12}{4}$$

Now solve the equation w=\frac{0±12}{4} when ± is plus. Divide 12 by 4.

$$w=3$$

Now solve the equation w=\frac{0±12}{4} when ± is minus. Divide -12 by 4.

$$w=-3$$

The equation is now solved.

$$w=3 w=-3$$