Free Online X-Game Calculator

What is the X-Game in Algebra?

The X-Game (also called the X-Factor method or Diamond Problem) is a mathematical puzzle used in middle and high school algebra to teach students how to factor quadratic trinomials ($ax^2 + bx + c$).

The rules of the X-Game are simple:

• Top Cell: Product of two numbers ($a \times b$).
• Bottom Cell: Sum of two numbers ($a + b$).
• Left & Right Cells: The two factor numbers ($a$ and $b$).

How to Solve X-Game Problems

Depending on which two values you start with, the solver applies different algebraic methods:

• Given Both Factors ($a$ and $b$): Multiply them to get the top product, and add them to get the bottom sum.
• Given One Factor and Product/Sum: Use basic division or subtraction to isolate the missing factor.
• Given Product ($P$) and Sum ($S$): Treat $a$ and $b$ as roots of the quadratic equation $x^2 – Sx + P = 0$ using the quadratic formula.

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