Popular Algebra Problems

Frequently Asked Questions

• How do I solve quadratic equations in algebra?

  

  Quadratic equations (e.g., \( ax^2 + bx + c = 0 \)) are solved using factoring, completing the square, or the quadratic formula:

  \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

  For example, to solve \( x^2 - 5x + 6 = 0 \):

  1. Factor into \( (x-2)(x-3) = 0 \).

  2. Solutions: \( x = 2 \) or \( x = 3 \).

  If factoring isn’t possible, use the quadratic formula. Always check the discriminant (\( b^2 - 4ac \)) to determine real/complex roots. This skill is critical for graphing parabolas and modeling real-world scenarios.

• What is the process for solving absolute value equations?

  

  Absolute value equations like \( |2x + 1| = 5 \) require splitting into two cases:

  1. Case 1: \( 2x + 1 = 5 \) → \( 2x = 4 \) → \( x = 2 \).

  2. Case 2: \( 2x + 1 = -5 \) → \( 2x = -6 \) → \( x = -3 \).

  Verify solutions by plugging them back: \( |2(2)+1| = 5 \) ✔️ and \( |2(-3)+1| = 5 \) ✔️. Note: Equations like \( |x| = -3 \) have no solution, as absolute values cannot equal negatives.

• How can ScanMath help you learn Algebra?

  

  ScanMath supports Algebra mastery through detailed explanations for linear equations, quadratic functions, polynomials, and inequalities.

  For instance, solving \(2x^2 - 5x + 3 = 0\) is simplified with factorization guidance or quadratic formula steps.

  It also covers complex topics like graphing linear inequalities, systems of equations, and logarithmic functions, mirroring resources like AoPS Introduction to Algebra.

  Whether preparing for exams (e.g., AMC 8/10) or tackling real-world applications, ScanMath’s interactive solver helps identify errors and reinforces algebraic reasoning.