You try.. solve using the quadratic formula4x2 = 9x − 2

Answer 1

To solve the equation 4x^2 = 9x - 2, we need to rewrite it in standard quadratic form (ax^2 + bx + c).

First, let's move all the terms to one side of the equation:
4x^2 - 9x + 2 = 0

Now, we can use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 4, b = -9, and c = 2. Substituting these values into the quadratic formula, we get:
x = (9 ± √((-9)^2 - 4(4)(2))) / (2(4))

Simplifying further:
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8

This gives us two possible solutions:
x = (9 + 7) / 8 = 16 / 8 = 2
or
x = (9 - 7) / 8 = 2 / 8 = 1/4

Therefore, the solutions to the equation 4x^2 = 9x - 2 are x = 2 and x = 1/4.