To solve the equation -12x^2 = 19x^4, we need to rearrange it into a standard form (quadratic equation) by setting it equal to zero:
19x^4 + 12x^2 = 0
Now, let's make a substitution to simplify this equation:
Let y = x^2
Therefore, the equation becomes:
19y^2 + 12y = 0
Now, we can factor out a common factor of y:
y(19y + 12) = 0
From this equation, we can see that either y = 0 or 19y + 12 = 0.
1. Setting y = 0:
x^2 = 0
x = 0
2. Solving 19y + 12 = 0:
19y + 12 = 0
19y = -12
y = -12/19
Now, substitute y back in terms of x^2:
x^2 = -12/19
x = ±√(-12/19)
x = ±(√12/√19)i
x = ±(2√3 / √19)i
Therefore, the solutions to the equation -12x^2 = 19x^4 are x = 0 and x Answer:
