Solve the following equation using the quadratic formula
2x^2+10x-17=0
The quadratic formula is given by x = (-b ± √(b^2 - 4ac)) / (2a), where the equation is in the form ax^2 + bx + c = 0.
For the equation 2x^2 + 10x - 17 = 0, we have a = 2, b = 10, and c = -17.
Plugging these values into the quadratic formula, we get:
x = (-10 ± √(10^2 - 4(2)(-17))) / (2(2))
Simplifying further:
x = (-10 ± √(100 + 136)) / 4
x = (-10 ± √236) / 4
Now we have two possible solutions:
x = (-10 + √236) / 4
x = (-10 - √236) / 4
So the solutions to the equation 2x^2 + 10x - 17 = 0 are:
x = (-10 + √236) / 4 and x = (-10 - √236) / 4.