Solve by Factoring x^4-13x^2+36=0

Problem

x4−13*x2+36=0

Solution

1. Identify the equation as a trinomial in quadratic form by letting u=x2 which transforms the equation into u2−13*u+36=0

2. Find two numbers that multiply to 36 and add to −13 which are −4 and −9

3. Factor the trinomial into two binomials using these values.

(x2−4)*(x2−9)=0

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

(x−2)*(x+2)*(x−3)*(x+3)=0

5. Set each individual factor equal to zero to solve for x

x−2=0⇒x=2

x+2=0⇒x=−2

x−3=0⇒x=3

x+3=0⇒x=−3

Final Answer

x=2,−2,3,−3

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