Factor 4x^2+49

Problem

4*x2+49

Solution

1. Identify the form of the expression as a sum of two squares, which follows the pattern a2+b2

2. Determine the square roots of each term, where a=√(,4*x2)=2*x and b=√(,49)=7

3. Apply the formula for factoring a sum of squares over the complex numbers, which is a2+b2=(a+b*i)*(a−b*i)

4. Substitute the values a=2*x and b=7 into the complex factoring formula.

Final Answer

4*x2+49=(2*x+7*i)*(2*x−7*i)

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