quadratic equation of 48x^2-32x-35=0 i need both answers you must use the quadratic formula
x = (32 +/- sqrt(32^2+4*48*35)]/96
To find the solutions of the quadratic equation 48x^2 - 32x - 35 = 0 using the quadratic formula, we can follow these steps:
1. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
2. In the given equation, the coefficients are:
a = 48, b = -32, and c = -35.
3. Plug these values into the quadratic formula:
x = (-(-32) ± √((-32)^2 - 4 * 48 * -35)) / (2 * 48)
Simplifying the formula:
x = (32 ± √(1024 + 6720)) / 96
x = (32 ± √7744) / 96
x = (32 ± 88) / 96
4. Now we can calculate the two possible solutions:
a) First, when plugging the positive square root:
x1 = (32 + 88) / 96
= 120 / 96
= 1.25
b) Second, when plugging the negative square root:
x2 = (32 - 88) / 96
= -56 / 96
= -0.5833
Therefore, the solutions to the quadratic equation 48x^2 - 32x - 35 = 0 are:
x1 ≈ 1.25 and x2 ≈ -0.5833.