Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
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].
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].
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.