Let's solve the equation [tex]\( 5x^3 + 7 = 34 \)[/tex] step-by-step.
1. Isolate the term with the variable [tex]\( x \)[/tex]:
- Start by subtracting 7 from both sides of the equation to get [tex]\( 5x^3 \)[/tex] by itself on one side.
[tex]\[
5x^3 + 7 - 7 = 34 - 7
\][/tex]
Simplifying this, we get:
[tex]\[
5x^3 = 27
\][/tex]
2. Isolate [tex]\( x^3 \)[/tex]:
- Next, divide both sides by 5 to further isolate [tex]\( x^3 \)[/tex].
[tex]\[
x^3 = \frac{27}{5}
\][/tex]
3. Solve for [tex]\( x \)[/tex] by taking the cube root of both sides:
- To find [tex]\( x \)[/tex], take the cube root of both sides of the equation.
[tex]\[
x = \sqrt[3]{\frac{27}{5}}
\][/tex]
4. Calculate the result:
- The value of [tex]\( \frac{27}{5} \)[/tex] is 5.4. Taking the cube root of 5.4, we get:
[tex]\[
x \approx 1.7544106429277195
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation [tex]\( 5x^3 + 7 = 34 \)[/tex] is approximately [tex]\( 1.7544106429277195 \)[/tex].
