Final answer:
To solve the equation 7ax³ + 5ax + 1 = 52, you can rearrange it to set it equal to zero. Then factor out a common factor of ax and set each factor equal to zero. By solving these equations, you will find the solutions to the equation.
Step-by-step explanation:
To solve the equation 7ax³ + 5ax + 1 = 52, we first need to rearrange it so that it is equal to zero.
7ax³ + 5ax + 1 - 52 = 0
Simplifying further:
7ax³ + 5ax - 51 = 0
Now, we can solve this equation either by factoring or by using the quadratic formula. In this case, factoring seems the more appropriate method.
Let's factor out a common factor of ax:
ax(7x² + 5) - 51 = 0
Now, we have two factors: ax and (7x² + 5).
We can set each factor equal to zero:
ax = 0
7x² + 5 = 0
Solving the first equation:
ax = 0
Since a is not equal to zero, we can divide both sides by a:
x = 0
Now, solving the second equation:
7x² + 5 = 0
Subtracting 5 from both sides:
7x² = -5
Dividing both sides by 7:
x² = -5/7
Taking the square root of both sides:
x = ±√(-5/7)
Therefore, the solutions to the equation are x = 0 and x = ±√(-5/7).