Solve the following equation using the quadratic formula.

Question

2x2−1=9x

Answer 1

To use the quadratic formula, we first need to write the equation in standard form:

2x^2 - 9x - 1 = 0

Now we can apply the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using:

x = (-b ± √(b^2 - 4ac))/(2a)

In this case, a = 2, b = -9, and c = -1. Substituting these values into the quadratic formula:

x = (-(-9) ± √((-9)^2 - 4(2)(-1)))/(2(2))
x = (9 ± √(81 + 8)) / 4
x = (9 ± √(89)) / 4

Therefore, the solutions to the equation are:

x = (9 + √89)/4

and

x = (9 - √89)/4