Factor x^2+49

Problem

x^2+49

Solution

1. Identify the expression as a sum of two squares, which follows the form a^2+b^2

2. Recognize that a sum of squares cannot be factored into linear factors using only real numbers.

3. Apply the complex number identity a^2+b^2=(a+b*i)*(a−b*i) where i=√(,−1)

4. Substitute a=x and b=7 into the identity since 49=7^2

5. Write the final factored form using the imaginary unit i

Final Answer

x^2+49=(x+7*i)*(x−7*i)

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