Answer:
To solve the equation 2x^2 - 5x + 1 = 3 for x, you can follow these steps:
Step 1: Rewrite the equation in standard quadratic form:
2x^2 - 5x + 1 - 3 = 0
2x^2 - 5x - 2 = 0
Step 2: Apply the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -5, and c = -2. Substituting these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4(2)(-2))) / (2(2))
x = (5 ± √(25 + 16)) / 4
x = (5 ± √41) / 4
So, the solutions for x are:
x = (5 + √41) / 4
x = (5 - √41) / 4
These are the exact solutions to the equation 2x^2 - 5x + 1 = 3.