Final answer:
The equation -34x⁴ = 14x⁷ is solved by dividing both sides by -34x⁴, resulting in a cube root operation to find that x = -1.346.
Step-by-step explanation:
To solve the equation -34x⁴ = 14x⁷, we first aim to get all terms involving x on one side of the equation to simplify the equation into a more recognizable form. Given that both sides of the equations are multiples of x, we can divide both sides by -34x⁴ to simplify the equation.
By dividing both sides by -34x⁴, we get:
1 = -rac{14}{34}x³
Next, we solve for x³ by multiplying both sides by the reciprocal of -rac{14}{34}, which simplifies to -rac{1}{2.4286}:
x³ = -2.4286
Now, we can take the cube root of both sides to solve for x:
x = ∛(-2.4286)
The cube root of a negative number is negative, so:
x = -1.346
Thus, the solution to the equation is x = -1.346.