SOLUTION: Dear tutor,Could you help me to solving this equation please?I do not have any idea to solve it! {{{x^4-13x^2+36=0}}}

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Question 201889: Dear tutor,Could you help me to solving this equation please?I do not have any idea to solve it!
x%5E4-13x%5E2%2B36=0
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-13x%5E2%2B36=0
(x^2-9)(x^2-4)=0
(x+3)(x-3)(x+2)(x-2)=0
x+3=0
x=-3 ans.
x-3=0
x=3 ans.
x+2=0
x=-2 ans.
x-2=0
x=2 ans.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-13x%5E2%2B36=0 Start with the given equation.


Let z=x%5E2. So z%5E2=x%5E4


z%5E2-13z%2B36=0 Replace x%5E4 with z%5E2. Replace x%5E2 with "z"


Notice that the quadratic z%5E2-13z%2B36 is in the form of Az%5E2%2BBz%2BC where A=1, B=-13, and C=36


Let's use the quadratic formula to solve for "z":


z+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


z+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%2836%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-13, and C=36


z+=+%2813+%2B-+sqrt%28+%28-13%29%5E2-4%281%29%2836%29+%29%29%2F%282%281%29%29 Negate -13 to get 13.


z+=+%2813+%2B-+sqrt%28+169-4%281%29%2836%29+%29%29%2F%282%281%29%29 Square -13 to get 169.


z+=+%2813+%2B-+sqrt%28+169-144+%29%29%2F%282%281%29%29 Multiply 4%281%29%2836%29 to get 144


z+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 144 from 169 to get 25


z+=+%2813+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


z+=+%2813+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


z+=+%2813+%2B+5%29%2F%282%29 or z+=+%2813+-+5%29%2F%282%29 Break up the expression.


z+=+%2818%29%2F%282%29 or z+=++%288%29%2F%282%29 Combine like terms.


z+=+9 or z+=+4 Simplify.


So the solutions in terms of "z" are z+=+9 or z+=+4


Now recall that we let z=x%5E2


So when z=9, x=sqrt%289%29=3 or x=-sqrt%289%29=-3


In other words, when z=9, x=3 or x=-3


So the first two solutions in terms of "x" are: x=3 or x=-3


Likewise, when z=4, x=sqrt%284%29=2 or x=-sqrt%284%29=-2


So when z=4, x=2 or x=-2


So the next two solutions in terms of "x" are: x=2 or x=-2


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Answer:


So the four solutions are:


x=3, x=-3, x=2 or x=-2