Prove polynomial identities and use them to solve or describe numerical relationships.
Use a factoring identity to solve a polynomial equation
Problem
Solve \(x^2~-~49~=~0\) over the real numbers using an identity.
Big Picture
What this problem is really about
Treat the equation as a factoring problem first and a solving problem second. Recognize the difference of squares, rewrite it as conjugate factors while keeping the product equal to zero, and then apply the zero-product property to both factors. Solving both resulting equations is essential because a square equation can have two real roots.
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