Answer: x = 2
Step 1.
In order to solve this non-linear equation, we need to move all the terms to the left side.
In x³ + 1 = 9...
- term 1, will be moved to the right side.
Notice that a term changes sign when it 'moves' from one side of the equation to the other.
Rewrite the equation like this: (x³ + 1) + (-1) = 9 + (-1)
Step 2.
Add x³ + 1 + (-1)
x³ + 1 + (-1) = 8
Now, x = 8.
Step 3.
In this non-linear equation, the variable needs to be isolated.
This is accomplished when both sides are exponentiated by the reciprocal of the variable's exponent, which in our example, 1/3 is equal to
Notice that since we exponentiated a simplified fraction with an odd denominator, only one solution has been created.
Rewrite the equation: [tex](x^3)^\frac{1}{3} =8^\frac{1}{3}[/tex]
Step 4.
We need to exponentiate the power.
The following rule is applied: [tex](A^B)^C=A^B^C[/tex]
According to the formula,
A = X
B = 3
C = 1/3
Rewrite the equation: [tex]x^3^\times^\frac{1}{3} =(2^3)^\frac{1}{3}[/tex]
Step 5.
We need to reduce this fraction, the 3 in x to the lowest terms.
This can be done by dividing out those factors that appear both in the numerator and in the denominator.
In our example, 3 is the common factor.
Rewrite the equation: [tex]x=2^\frac{3}{3}[/tex]
Step 6.
Lastly, we'll need to do the same thing as we did in step 5. Reduce the fraction in [tex]x=2\frac{3}{3}[/tex]. This can be done by dividing out those factors that appear both in the numerator and in the denominator.
Hence, the common factor is 3 since it occurs both in the numerator and the denominator.
Hence, x = 2.
