Certainly! Let's start with an initial quadratic equation and simplify it step-by-step to demonstrate how it reduces to the form [tex]\(7x^2 - 25x - 300 = 0\)[/tex].
Assume we start with the equation:
[tex]\[14x^2 - 50x - 600 = 0.\][/tex]
We need to simplify this equation. One way to simplify it is by dividing each term by 2. Let's proceed with this step-by-step:
1. Initial Equation:
[tex]\[14x^2 - 50x - 600 = 0.\][/tex]
2. Division by 2:
We divide every term in the equation by 2. The process is as follows:
[tex]\[
\frac{14x^2}{2} - \frac{50x}{2} - \frac{600}{2} = \frac{0}{2}
\][/tex]
3. Simplifying Each Term:
[tex]\[
\frac{14x^2}{2} = 7x^2
\][/tex]
[tex]\[
\frac{50x}{2} = 25x
\][/tex]
[tex]\[
\frac{600}{2} = 300
\][/tex]
[tex]\[
\frac{0}{2} = 0
\][/tex]
4. Putting It All Together:
Substitute these simplified terms back into the equation:
[tex]\[
7x^2 - 25x - 300 = 0
\][/tex]
Hence, the original quadratic equation [tex]\(14x^2 - 50x - 600 = 0\)[/tex] simplifies to:
[tex]\[7x^2 - 25x - 300 = 0.\][/tex]
Therefore, we've shown that the equation simplifies to [tex]\(7x^2 - 25x - 300 = 0\)[/tex].
