Radical Equation Solver Calculator

Work out radical equation solver instantly with clear inputs, formula shown and shareable results.

About Radical Equation Solver Calculator

Squaring both sides removes the radical, giving ax + b = c² and hence x = (c² − b)/a. Squaring is not reversible, so the answer must always be substituted back to rule out extraneous roots.

Formula

Radical equation

√(ax + b) = c ⇒ ax + b = c² ⇒ x = (c² − b)/a, valid only if c ≥ 0

Worked example

With the default values below, Radical Equation Solver Calculator returns x of 11.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Coefficient a in √(ax + b) = c: 2
Constant b: 3
Right-hand side c: 5

Results

x: 11.00000000
c² after squaring both sides: 25.00000000
Value inside the root at the solution: 25.00000000
Check: Genuine solution, the radicand is non-negative

Step by step

1Values used
2Radical equation
3x= 11.00000000
4c² after squaring both sides= 25.00000000
5Value inside the root at the solution= 25.00000000
6Check= Genuine solution, the radicand is non-negative

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Solve √(2x + 3) = 5.

2x + 3 = 25, so x = 11, and √25 = 5 confirms it.

What is an extraneous solution?

One produced by squaring that fails in the original equation, typically because it makes a square root equal a negative number.