Solve (-5b)^2-4(4)(49)=0

$$( - 5 b ) ^ { 2 } - 4 ( 4 ) ( 49 ) = 0$$

Solve for b

$$b = -\frac{28}{5} = -5\frac{3}{5} = -5.6$$

$$b = \frac{28}{5} = 5\frac{3}{5} = 5.6$$

Steps Using Difference of Squares

Expand \left(-5b\right)^{2}.

$$\left(-5\right)^{2}b^{2}-4\times 4\times 49=0$$

Calculate -5 to the power of 2 and get 25.

$$25b^{2}-4\times 4\times 49=0$$

Multiply 4 and 4 to get 16.

$$25b^{2}-16\times 49=0$$

Multiply 16 and 49 to get 784.

$$25b^{2}-784=0$$

Consider 25b^{2}-784. Rewrite 25b^{2}-784 as \left(5b\right)^{2}-28^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5b-28\right)\left(5b+28\right)=0$$

To find equation solutions, solve 5b-28=0 and 5b+28=0.

$$b=\frac{28}{5} b=-\frac{28}{5}$$

Steps by Finding Square Root

Expand \left(-5b\right)^{2}.

$$\left(-5\right)^{2}b^{2}-4\times 4\times 49=0$$

Calculate -5 to the power of 2 and get 25.

$$25b^{2}-4\times 4\times 49=0$$

Multiply 4 and 4 to get 16.

$$25b^{2}-16\times 49=0$$

Multiply 16 and 49 to get 784.

$$25b^{2}-784=0$$

Add 784 to both sides. Anything plus zero gives itself.

$$25b^{2}=784$$

Divide both sides by 25.

$$b^{2}=\frac{784}{25}$$

Take the square root of both sides of the equation.

$$b=\frac{28}{5} b=-\frac{28}{5}$$

Steps Using the Quadratic Formula

Expand \left(-5b\right)^{2}.

$$\left(-5\right)^{2}b^{2}-4\times 4\times 49=0$$

Calculate -5 to the power of 2 and get 25.

$$25b^{2}-4\times 4\times 49=0$$

Multiply 4 and 4 to get 16.

$$25b^{2}-16\times 49=0$$

Multiply 16 and 49 to get 784.

$$25b^{2}-784=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -784 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 25\left(-784\right)}}{2\times 25}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 25\left(-784\right)}}{2\times 25}$$

Multiply -4 times 25.

$$b=\frac{0±\sqrt{-100\left(-784\right)}}{2\times 25}$$

Multiply -100 times -784.

$$b=\frac{0±\sqrt{78400}}{2\times 25}$$

Take the square root of 78400.

$$b=\frac{0±280}{2\times 25}$$

Multiply 2 times 25.

$$b=\frac{0±280}{50}$$

Now solve the equation b=\frac{0±280}{50} when ± is plus. Reduce the fraction \frac{280}{50} to lowest terms by extracting and canceling out 10.

$$b=\frac{28}{5}$$

Now solve the equation b=\frac{0±280}{50} when ± is minus. Reduce the fraction \frac{-280}{50} to lowest terms by extracting and canceling out 10.

$$b=-\frac{28}{5}$$

The equation is now solved.

$$b=\frac{28}{5} b=-\frac{28}{5}$$