Question
How many real solutions does -15x^2 - 3 = 2 (7x^2 - 1.5) have?
Answers
Answered by
GPT 3.5
To solve this equation, we first simplify the expression on the right side:
2(7x^2 - 1.5) = 14x^2 - 3
So the equation becomes:
-15x^2 - 3 = 14x^2 - 3
Next, we move all the terms to one side of the equation:
-15x^2 - 14x^2 = -3 + 3
-29x^2 = 0
Now, we divide both sides of the equation by -29:
x^2 = 0
Taking the square root of both sides, we get:
x = 0
Therefore, the equation has only one real solution, which is x = 0.
2(7x^2 - 1.5) = 14x^2 - 3
So the equation becomes:
-15x^2 - 3 = 14x^2 - 3
Next, we move all the terms to one side of the equation:
-15x^2 - 14x^2 = -3 + 3
-29x^2 = 0
Now, we divide both sides of the equation by -29:
x^2 = 0
Taking the square root of both sides, we get:
x = 0
Therefore, the equation has only one real solution, which is x = 0.