Step-by-Step Problem Solver

Type a problem and get a worked solution, step by step. Solutions are written by AI and can contain mistakes, so check each step. Each one uses AI credits.

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Problem StatementExample

Solve the quadratic equation: 2x^2 - 7x + 3 = 0

Approach:We will solve by factoring the quadratic trinomial into two linear binomials (2x - 1)(x - 3) = 0 and applying the Zero Product Property.

Step-by-step working (3 steps)

Identify Coefficients & AC Product

For the general quadratic form $ax^2 + bx + c = 0$ , we identify: $a = 2$ , $b = -7$ , and $c = 3$ .

a \cdot c = 2 \times 3 = 6, \quad b = -7

Justification:

Find two integers that multiply to $ac = 6$ and sum to $b = -7$ . These numbers are $-6$ and $-1$ .

Split Middle Term & Factor by Grouping

Decompose $-7x$ as $-6x - x$ and group terms pair-wise:

2x^2 - 6x - x + 3 = 2x(x - 3) - 1(x - 3) = (2x - 1)(x - 3)

Justification:

Extract the common binomial factor $(x - 3)$ from both grouped pairs.

Invoke Zero Product Property

Set each independent linear factor equal to zero and isolate $x$ :

2x - 1 = 0 \implies x = \frac{1}{2}, \quad x - 3 = 0 \implies x = 3

Justification:

The two distinct real roots of the quadratic equation are $x = \frac{1}{2}$ and $x = 3$ .

Final answer

x = \frac{1}{2}, \quad x = 3

GraphFormula: 2*x^2 - 7*x + 3

Canvas: f(x) = 2*x^2 - 7*x + 3

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About this tool: Step-by-Step Solver

What it does: A solver that writes out a worked solution to a math problem, step by step, with the approach stated first.
How to use it: Type the problem and read the steps in order. From a finished solution you can go on to practice problems like it, a quiz or flashcards.
What to check: Solutions are written by AI and can contain mistakes, so check each step rather than copying the last line. Each solution uses AI credits from your account.