Final answer:
The equation provided by the student results in a quadratic equation after simplification. The quadratic formula can be used to find the solutions, but the constants provided earlier are not applicable to the equation in the question.
Step-by-step explanation:
The original equation given by the student, 25(x²-5)+14=10, is indeed a quadratic equation once it is simplified. To solve it, you will need to distribute the 25 into the binomial and subtract 10 from both sides to get the equation into the standard form of at² + bt + c = 0.
Let's solve the student's equation step-by-step:
- Distribute the 25 into the binomial: 25x² - 125 + 14 = 10
- Combine like terms and subtract 10 from both sides to get the equation to 0: 25x² - 125 + 14 - 10 = 0, which simplifies to 25x² - 121 = 0
- Finally, use the quadratic formula, where a = 25, b = 0, and c = -121, to find the solution for x.
However, the information provided to solve using a = 4.90, b = 14.3, c = -20.0 does not match the equation given by the student, and thus cannot be applied directly without clarification or correction.