Solve 49w^2-4=0

$$49 w ^ { 2 } - 4 = 0$$

Solve for w

$$w=\frac{2}{7}\approx 0.285714286$$

$$w=-\frac{2}{7}\approx -0.285714286$$

Steps Using Difference of Squares

Consider 49w^{2}-4. Rewrite 49w^{2}-4 as \left(7w\right)^{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).

$$\left(7w-2\right)\left(7w+2\right)=0$$

To find equation solutions, solve 7w-2=0 and 7w+2=0.

$$w=\frac{2}{7} w=-\frac{2}{7}$$

Steps by Finding Square Root

Add 4 to both sides. Anything plus zero gives itself.

$$49w^{2}=4$$

Divide both sides by 49.

$$w^{2}=\frac{4}{49}$$

Take the square root of both sides of the equation.

$$w=\frac{2}{7} w=-\frac{2}{7}$$

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.

$$49w^{2}-4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 49\left(-4\right)}}{2\times 49}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 49\left(-4\right)}}{2\times 49}$$

Multiply -4 times 49.

$$w=\frac{0±\sqrt{-196\left(-4\right)}}{2\times 49}$$

Multiply -196 times -4.

$$w=\frac{0±\sqrt{784}}{2\times 49}$$

Take the square root of 784.

$$w=\frac{0±28}{2\times 49}$$

Multiply 2 times 49.

$$w=\frac{0±28}{98}$$

Now solve the equation w=\frac{0±28}{98} when ± is plus. Reduce the fraction \frac{28}{98} to lowest terms by extracting and canceling out 14.

$$w=\frac{2}{7}$$

Now solve the equation w=\frac{0±28}{98} when ± is minus. Reduce the fraction \frac{-28}{98} to lowest terms by extracting and canceling out 14.

$$w=-\frac{2}{7}$$

The equation is now solved.

$$w=\frac{2}{7} w=-\frac{2}{7}$$