Problem

Solve \(4x^{2}-49=0\) by identifying the two squared quantities. Write the conjugate-factor equation, solve both linear factors, and report the exact zeros.

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squares=(2x)² and7²; factors=(2x−7)(2x+7)=0; branches=2x−7=0,2x+7=0; zeros=-7,7; substitution check=fails when leading coefficients or factor signs are ignored

squares=(2x)² and7²; factors=(2x−7)(2x+7)=0; branches=2x=±7; zeros=x=7/2,-7/2; check=4·49/4−49=0

squares=(2x)² and7²; factors=(2x−7)(2x+7)=0; zero-product branch=positive branch only; zero=x=7/2; check=positive root works

squares=(2x)² and7²; factors=uses the same sign twice or leaves nested factors unsimplified; zero-product branches=incomplete; zeros=incomplete; expansion check=produces a middle term or unfinished form

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Solve \(4x^{2}-49=0\) by identifying the two squared quantities. Write the conjugate-factor equation, solve both linear factors, and report the exact zeros.

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