Q 6.96 - Intermediate Algebra

Question

Solve $123b=-6-60b^2$ 

Step-by-Step Solution

Answer

The value is $-\frac{1}{20},-2$

Step 1: Given information

Given the equation $123b=-6-60b^2$$123b=-6-60b^2$

Step 2: Write the quadratic equation in standard form

The equation is written as follows;

$$\begin{gathered} 123b=-6-60b^2 \\ -60b^2-123b-6=0 \\ 60b^2+123b+6=0 \\ 3(20b^2+41b+2)=0 \end{gathered}$$

Step 3: Use zero factor property and calculate the value

Further solving, we get

$$\begin{gathered} 20b^2+41b+2=0 \\ 20b^2+40b+b+2=0 \\ 20b(b+2)+1(b+2)=0 \\ (20b+1)(b+2)=0 \\ b=-\frac{1}{20},-2 \end{gathered}$$

Step 4: Check the value

Checking, we get

$$\begin{gathered} 123(-\frac{1}{20})=-6-60{(-\frac{1}{20})}^2-\frac{123}{20}=-6-\frac{60}{400} \\ \frac{-123}{20}=-6-\frac{3}{20} \\ \frac{-123}{20}=\frac{-123}{20} \end{gathered}$$

Step 5: Checking for another point

Checking, we get

$$\begin{gathered} 123(-2)=-6-60{(-2)}^2-246=-6-240 \\ -246=-246 \end{gathered}$$

So the value is correct