Solving a Radical Equation

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.

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.