Solve x² − 9 = 0
The solutions of x² − 9 = 0 are x = 3 and x = −3.
Problem
Answer
Step-by-step solution
Step 1: Factor
x² − 9 = (x − 3)(x + 3).
Step 2: Zero product
x − 3 = 0 or x + 3 = 0.
Step 3: Solutions
x = 3 or x = −3.
Why this works
A difference of squares a² − b² factors as (a − b)(a + b). Taking square roots of x² = 9 also produces ±3; omitting the negative root is a common error.
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Frequently asked questions
Is x = 3 the only solution?
No. Squaring erases sign, so both 3 and −3 satisfy x² = 9.