College Algebra / Unit 4 Alg 220 worked example, 60 to 90 seconds
Solving a Radical Equation
The idea
Solving a radical equation means isolating the radical, raising both sides to the index's power, solving what remains, and checking every candidate in the original equation.
In practice
Solve √(2x + 3) = x. The radical stands alone. Square both sides: 2x + 3 = x². Standard form: x² − 2x − 3 = 0, which factors as (x − 3)(x + 1) = 0, giving candidates 3 and −1. Now the audit, in the original: at x = 3, √9 = 3 — true. At x = −1, √1 = 1, and 1 ≠ −1 — extraneous, discard. The solution is x = 3 alone. The squaring honestly earned both candidates; the original honestly kept one. Two radicals mean two rounds of isolate-and-raise, with the audit still last.
Where people slip
A candidate that fails the original is discarded without apology; the check is the verdict.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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