Solve 25b^2-16=0

$$25 b ^ { 2 } - 16 = 0$$

Solve for b

$$b=\frac{4}{5}=0.8$$

$$b=-\frac{4}{5}=-0.8$$

Steps Using Difference of Squares

Consider 25b^{2}-16. Rewrite 25b^{2}-16 as \left(5b\right)^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5b-4\right)\left(5b+4\right)=0$$

To find equation solutions, solve 5b-4=0 and 5b+4=0.

$$b=\frac{4}{5} b=-\frac{4}{5}$$

Steps by Finding Square Root

Add 16 to both sides. Anything plus zero gives itself.

$$25b^{2}=16$$

Divide both sides by 25.

$$b^{2}=\frac{16}{25}$$

Take the square root of both sides of the equation.

$$b=\frac{4}{5} b=-\frac{4}{5}$$

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.

$$25b^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 25\left(-16\right)}}{2\times 25}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 25\left(-16\right)}}{2\times 25}$$

Multiply -4 times 25.

$$b=\frac{0±\sqrt{-100\left(-16\right)}}{2\times 25}$$

Multiply -100 times -16.

$$b=\frac{0±\sqrt{1600}}{2\times 25}$$

Take the square root of 1600.

$$b=\frac{0±40}{2\times 25}$$

Multiply 2 times 25.

$$b=\frac{0±40}{50}$$

Now solve the equation b=\frac{0±40}{50} when ± is plus. Reduce the fraction \frac{40}{50} to lowest terms by extracting and canceling out 10.

$$b=\frac{4}{5}$$

Now solve the equation b=\frac{0±40}{50} when ± is minus. Reduce the fraction \frac{-40}{50} to lowest terms by extracting and canceling out 10.

$$b=-\frac{4}{5}$$

The equation is now solved.

$$b=\frac{4}{5} b=-\frac{4}{5}$$