Solve an Equation With Two Radicals

An equation of the form \( \sqrt{ax + b} = \sqrt{cx + d} + e \) is solved by isolating radicals and squaring both sides twice.

📌 Important: Squaring may introduce extraneous solutions, so all candidates must be verified in the original equation.

The solutions below are given in exact simplified form (fractions reduced, radicals simplified).

✧ Solve: √(ax + b) = √(cx + d) + e ✧

Enter coefficients a, b, c, d, e

Equation: \( \sqrt{ax + b} = \sqrt{cx + d} + e \)





\( \sqrt{2x + 3} = \sqrt{x + 4} - 1 \)
⚠️ a and c should be non-zero. The equation is solved step by step with exact simplified values.
📐 Solution(s) to the Equation
\( x = 6 \)

📖 Step-by-Step Solution

STEP 1: Square both sides and simplify
STEP 2: Isolate the remaining radical term
STEP 3: Square both sides again and simplify to quadratic form
STEP 4: Solve the quadratic equation (exact simplified values)
STEP 5: Verify solutions in the original equation (check for extraneous)
💡 Important Note
Squaring both sides of an equation can introduce extraneous solutions. Always verify each candidate in the original equation. Also, radicands must be non-negative for real solutions.
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