Let's solve the equation step by step:
1/2x^2 + 11.5 + 2x^2 = 2x^2 - 10
Combine like terms:
(1/2 + 2)x^2 + 11.5 = 2x^2 - 10
(5/2)x^2 + 11.5 = 2x^2 - 10
Now, subtract 2x^2 from both sides:
(5/2)x^2 - 2x^2 + 11.5 = -10
(5/2 - 2)x^2 + 11.5 = -10
(5/2 - 4/2)x^2 + 11.5 = -10
(1/2)x^2 + 11.5 = -10
Subtract 11.5 from both sides:
(1/2)x^2 = -10 - 11.5
(1/2)x^2 = -21.5
Now, multiply by 2 to get rid of the fraction:
x^2 = -43
Take the square root of both sides:
x = ±√(-43)
As the square root of a negative number is not a real number, the solution to the equation is not possible in the real number system.
Let's solve the equation step by step:
1/2x^2 + 11.5 + 2x^2 = 2x^2 - 10
Combine like terms:
(1/2 + 2)x^2 + 11.5 = 2x^2 - 10
(5/2)x^2 + 11.5 = 2x^2 - 10
Now, subtract 2x^2 from both sides:
(5/2)x^2 - 2x^2 + 11.5 = -10
(5/2 - 2)x^2 + 11.5 = -10
(5/2 - 4/2)x^2 + 11.5 = -10
(1/2)x^2 + 11.5 = -10
Subtract 11.5 from both sides:
(1/2)x^2 = -10 - 11.5
(1/2)x^2 = -21.5
Now, multiply by 2 to get rid of the fraction:
x^2 = -43
Take the square root of both sides:
x = ±√(-43)
As the square root of a negative number is not a real number, the solution to the equation is not possible in the real number system.