Find all real solutions of the equation. x^{5}+8x^{2}=0

Ann Tice 2021-11-21 Answered
Find all real solutions of the equation.
\(\displaystyle{x}^{{{5}}}+{8}{x}^{{{2}}}={0}\)

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Expert Answer

Volosoyx
Answered 2021-11-22 Author has 1441 answers
Step 1
To find all the real solution of the equation: \(\displaystyle{x}^{{{5}}}+{8}{x}^{{{2}}}={0}\)
Solution:
Given equation is \(\displaystyle{x}^{{{5}}}+{8}{x}^{{{2}}}={0}\).
Solving the given equation.
\(\displaystyle{x}^{{{5}}}+{8}{x}^{{{2}}}={0}\)
\(\displaystyle{x}^{{{2}}}{\left({x}^{{{3}}}+{8}\right)}={0}\)
\(\displaystyle{x}^{{{2}}}={0}\ {\quad\text{or}\quad}\ {x}^{{{3}}}+{8}={0}\)
\(\displaystyle{x}={0}\ {\quad\text{or}\quad}\ {x}^{{{3}}}=-{8}\)
x=0 or x=-2
Therefore, solution of the given equation are x={−2,0}.
Step 2
Hence, required solution is x={−2,0}.
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Befoodly
Answered 2021-11-23 Author has 945 answers
Simplifying
\(\displaystyle{x}^{{{5}}}+{8}{x}^{{{2}}}={0}\)
Reorder the terms:
\(\displaystyle{8}{x}^{{{2}}}+{x}^{{{5}}}={0}\)
Solving
\(\displaystyle{8}{x}^{{{2}}}+{x}^{{{5}}}={0}\)
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '\(\displaystyle{x}^{{{2}}}\)'.
\(\displaystyle{x}^{{{2}}}{\left({8}+{x}^{{{3}}}\right)}={0}\)
Set the factor '\(\displaystyle{x}^{{{2}}}\)' equal to zero and attempt to solve:
Simplifying
\(\displaystyle{x}^{{{2}}}={0}\)
Solving
\(\displaystyle{x}^{{{2}}}={0}\)
Move all terms containing x to the left, all other terms to the right.
Simplifying
\(\displaystyle{x}^{{{2}}}={0}\)
Take the square root of each side:
x = {0}
Set the factor '\(\displaystyle{\left({8}+{x}^{{{3}}}\right)}\)' equal to zero and attempt to solve:
Simplifying
\(\displaystyle{8}+{x}^{{{3}}}={0}\)
Solving
\(\displaystyle{8}+{x}^{{{3}}}={0}\)
Move all terms containing x to the left, all other terms to the right.
Add '-8' to each side of the equation.
\(\displaystyle{8}+-{8}+{x}^{{{3}}}={0}+-{8}\)
Combine like terms: 8 + -8 = 0
\(\displaystyle{0}+{x}^{{{3}}}={0}+-{8}\)
\(\displaystyle{x}^{{{3}}}={0}+-{8}\)
Combine like terms: 0 + -8 = -8
\(\displaystyle{x}^{{{3}}}=-{8}\)
Simplifying
\(\displaystyle{x}^{{{3}}}=-{8}\)
Solution
x = {0}
0

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