Solving √(2x + 3) = x - 1

Algebra 1 · Axiom Academy

EXAMPLE Solving a Radical Equation Isolate the radical, square both sides, solve the quadratic, then check every candidate for extraneous roots. Solve the radical equation for all real values of x , and verify which solutions are valid. Nice work. You solved a radical equation end to end and caught an extraneous root that squaring slipped in. Isolate the radical first, then square both sides to remove it. Squaring can introduce extraneous solutions that satisfy the squared equation but not the original. Always check every candidate by substituting back into the original equation. A principal square root is never negative, so the side it equals cannot be negative either. Reach for the quadratic formula when the resulting quadratic does not factor nicely. Here checked out, but was extraneous: it made the right side negative while the left side, a square root, must stay non-negative.

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