Final answer:
The nearest tenth solution of the equation 2x^2 + x - 31 = 0is 3.5.
Step-by-step explanation:
To solve the equation 2x^2 + x - 31 = 0 to the nearest tenth, we can use the quadratic formula.
For an equation of the form ax^2 + bx + c = 0, the quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / (2a).
Applying this formula to our equation, where a = 2, b = 1, and c = -31, we get:
x = (-1 +/- sqrt(1^2 - 4(2)(-31))) / (2(2))
x = (-1 +/- sqrt(1 + 248)) / 4
x = (-1 +/- sqrt(249)) / 4
Using a calculator, we find that the two possible solutions to the equation are approximately -4.5 and 3.5. To the nearest tenth, the solution is 3.5.