Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Solve a difference-of-squares equation by factoring and using the zero-product property
Problem
Solve \(x^{2}-49=0\) by factoring it as a difference of squares. Write both conjugate factors and apply the zero-product property to retain both solutions.
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What this problem is really about
This quadratic has the special form one square minus another square. We’ll rewrite the constant as a square, factor the difference into conjugate binomials, and use the zero-product property on both factors so the two opposite-sign solutions are both retained.
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