Solve by Factoring x^4-50x^2+49=0

Problem

x4−50*x2+49=0

Solution

1. Identify the equation as a trinomial in quadratic form by letting u=x2 which transforms the equation into u2−50*u+49=0

2. Factor the quadratic expression by finding two numbers that multiply to 49 and add to −50 which are −49 and −1

3. Substitute back x2 for u to write the factored form in terms of x

(x2−49)*(x2−1)=0

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

(x−7)*(x+7)*(x−1)*(x+1)=0

5. Solve for x by setting each individual factor equal to zero.

x−7=0⇒x=7

x+7=0⇒x=−7

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x={−7,−1,1,7}

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