Solvecoon

Equation solver

Every line
of the rearrangement.

An equation solver that prints x = 4 is a calculator with extra steps. What you need is the sequence of legal moves that got there, and the substitution at the end that proves it was legal.

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Free to try — 5 solves every day. No credit card.

How it works

1

Select or snap the equation

Typed equations select fine. Anything with a fraction bar or a radical is faster to snap.

2

Read the moves

Each step names the operation applied to both sides, not just the result of applying it.

3

See the check

The solution is substituted back into the original equation, which is where extraneous roots die.

What it handles

Linear

Brackets, fractional coefficients, and variables on both sides.

Quadratic

Factoring, completing the square, and the formula, with the discriminant read first.

Simultaneous

Substitution, elimination, and when a system has no solution or infinitely many.

Rational

Common denominators, restricted values, and the extraneous solutions they create.

Radical and absolute value

Both cases written out, and the check that eliminates the invalid one.

Exponential and logarithmic

Log laws, changing base, and the domain restriction that rules out negative arguments.

A real one, worked out

This is the shape of every answer: the result first, then the reasoning that got there.

Question

Solve: 2x^2 - 7x + 3 = 0

Answer

x = 3 or x = 1/2

Steps

  1. 1Check the discriminant first: b^2 - 4ac = 49 - 24 = 25. It is a perfect square, so the quadratic factors.
  2. 2Find two numbers multiplying to a x c = 6 and adding to -7: they are -1 and -6.
  3. 3Split the middle term: 2x^2 - 6x - x + 3 = 0.
  4. 4Factor in pairs: 2x(x - 3) - 1(x - 3) = 0.
  5. 5Factor out the bracket: (2x - 1)(x - 3) = 0.
  6. 6Set each factor to zero: 2x - 1 = 0 gives x = 1/2, and x - 3 = 0 gives x = 3.

Reading the discriminant before choosing a method saves time: a perfect square means it factors, so the formula is unnecessary work.

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Substituting back is not optional. It is the only step that proves you are right.

What it will not do

  • It will not be used during a graded assessment.
  • It will not solve an equation you transcribed wrong. Capture the original.
  • It will not always use your textbook's method. Name the method you want.
  • It will not skip the domain check on rational and radical equations, even when you want a shortcut.

Solvecoon is a study aid, not an answer machine. Exams, graded quizzes, and proctored tests are off limits — see the acceptable use policy.

Questions people ask

Does it show all solutions?
Yes, including both roots of a quadratic, both cases of an absolute value, and the general solution of a trig equation when one is asked for.
What about extraneous solutions?
Rational and radical equations are checked against the original equation, and any solution that breaks a denominator or produces a negative under an even root is discarded with a reason.
Can it factor rather than use the formula?
It picks the shortest valid route and says why. Ask for a specific method and it will redo the working that way.
Does it work on inequalities?
Yes, including the sign flip when both sides are multiplied or divided by a negative, with the answer given in interval notation.
Solvecoon raccoon mascot

Stuck on something?

Select it or snap it — Solvecoon understands it.

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Free to try — 5 solves every day. No credit card.