Solve by Factoring x^4-29x^2+100=0

Problem

x4−29*x2+100=0

Solution

1. Identify the equation as a trinomial in quadratic form by letting u=x2 which transforms the equation into u2−29*u+100=0

2. Find factors of the constant term 100 that add up to the middle coefficient −29 These factors are −25 and −4

3. Factor the trinomial into two binomials using the identified factors.

(x2−25)*(x2−4)=0

4. Apply the difference of squares formula a2−b2=(a−b)*(a+b) to both factors.

(x−5)*(x+5)*(x−2)*(x+2)=0

5. Set each factor to zero using the zero product property to solve for x

x−5=0⇒x=5

x+5=0⇒x=−5

x−2=0⇒x=2

x+2=0⇒x=−2

Final Answer

x={−5,−2,2,5}

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