To solve the equation 2x^2 + 12x - 110, we can use the quadratic formula or factoring method.
1. Quadratic Formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, the coefficients are:
a = 2
b = 12
c = -110
Plugging these values into the quadratic formula, we get:
x = (-12 ± √(12^2 - 4(2)(-110))) / (2(2))
Simplifying further:
x = (-12 ± √(144 + 880)) / 4
x = (-12 ± √1024) / 4
x = (-12 ± 32) / 4
Now, we have two possible solutions:
x1 = (-12 + 32) / 4 = 20 / 4 = 5
x2 = (-12 - 32) / 4 = -44 / 4 = -11
Therefore, the solutions to the equation 2x^2 + 12x - 110 are x = 5 and x = -11.
2. Factoring:
Another method to solve the equation is by factoring. However, in this case, the equation cannot be easily factored.
Using the quadratic formula is the most appropriate method to find the solutions.
I hope this helps, Let me know if you have any further questions.