Solve 49x^2-sqrt{16}=0

$$49 { x }^{ 2 } - \sqrt{ 16 } =0$$

Solve for x

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

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

Steps Using Difference of Squares

Calculate the square root of 16 and get 4.

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

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

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

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

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

Steps by Finding Square Root

Calculate the square root of 16 and get 4.

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

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

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

Divide both sides by 49.

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

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate the square root of 16 and get 4.

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

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}.

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

Square 0.

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

Multiply -4 times 49.

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

Multiply -196 times -4.

$$x=\frac{0±\sqrt{784}}{2\times 49}$$

Take the square root of 784.

$$x=\frac{0±28}{2\times 49}$$

Multiply 2 times 49.

$$x=\frac{0±28}{98}$$

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

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

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

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

The equation is now solved.

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