x⁴ - 169 x² + 3600 = 0
find x.
Answers
Answer:
x = 5, x = -5
Explanation:
Simplifying
x4 + -169x2 + 3600 = 0
Reorder the terms:
3600 + -169x2 + x4 = 0
Solving
3600 + -169x2 + x4 = 0
Solving for variable 'x'.
Factor a trinomial.
(25 + -1x2)(144 + -1x2) = 0
Factor a difference between two squares.
((5 + x)(5 + -1x))(144 + -1x2) = 0
Factor a difference between two squares.
((12 + x)(12 + -1x))(5 + x)(5 + -1x) = 0
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:
Simplifying
5 + x = 0
Solving
5 + x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5
Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5
Combine like terms: 0 + -5 = -5
x = -5
Simplifying
x = -5
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:
Simplifying
5 + -1x = 0
Solving
5 + -1x = 0
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5
Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5
Combine like terms: 0 + -5 = -5
-1x = -5
Divide each side by '-1'.
x = 5
Simplifying
x = 5
Step-by-step explanation:
question is x⁴ - 169
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