solve for x in the following expression using the quadratic formula
3x^2 + 29x - 8.5=0
a = 3
b = 29
c = -8.5
You can find the quadratic by a google search. It is sort of hard to write it here.. but here it is in words
minus b plus or minus the square root of b-squared -4ac all over 2a. This will give you 2 values for x.
To solve for x in the quadratic equation 3x^2 + 29x - 8.5 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 3, b = 29, and c = -8.5. Plugging these values into the quadratic formula, we get:
x = (-29 ± √(29^2 - 4 * 3 * -8.5)) / (2 * 3)
Simplifying further:
x = (-29 ± √(841 + 102)) / 6
x = (-29 ± √943) / 6
The square root of 943 is approximately 30.71. So the two solutions for x are:
x = (-29 + 30.71) / 6 ≈ 0.12
x = (-29 - 30.71) / 6 ≈ -9.52
Therefore, the solutions for the quadratic equation 3x^2 + 29x - 8.5 = 0 are approximately x = 0.12 and x ≈ -9.52.