Final answer:
To solve the quadratic equation 7x² - 3x + 5 = 0, we apply the quadratic formula. By identifying the coefficients and substituting them into the formula, we can calculate the solutions for x. It's critical to follow the steps and check the final answer for accuracy.
Step-by-step explanation:
To solve the quadratic equation 7x² - 3x + 5 = 0, we can use the quadratic formula:
x = √(-b ± √(b²-4ac))/(2a)
In this equation, 'a' is 7, 'b' is -3, and 'c' is 5. Substituting these values into the formula provides us with the solutions for x.
- Rearrange the equation to make sure it is in the form ax² + bx + c = 0, which is already done for 7x² - 3x + 5 = 0.
- Identify the coefficients a = 7, b = -3, and c = 5.
- Substitute these values into the quadratic formula and calculate the value under the radical (discriminant), which is b² - 4ac.
- Solve for x using the formula and simplify the resulting expressions.
- Check the answer to ensure it is reasonable based on the values of a, b, and c.
It is important to follow these steps carefully to arrive at the correct solution for the quadratic equation.