Solving quadratic equations

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Quadratic equation solving methods

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Solving quadratic equations

  1. 1. Arnulfo Peña Herma Araujo
  2. 2. What is a quadratic equation?  The name quadratic zome from “squad” meaning square, the variable get squared (over 2)  The standard form of a quadratic equation is: ax´2 + bx + c  The assumptions are:  a, b and c are known values. a can't be 0.  "x" is the variable or unknown (you don't know it yet).
  3. 3. Hidden quadratic equations
  4. 4. How to solve quadratic equations  There are 3 ways to find the solutions:  1. You can Factor the Quadratic (find what to multiply to make the Quadratic Equation)  2. You can Complete the Square  3. You can use the special Quadratic Formula:
  5. 5. Solving quadratic equations by factorizing  Having an easy quadratic formula, factorizing become a easy and fast method:  Having: x2 + 10x + 25  Can factorized as (x+5) (x+5)  Now by making each equation equal “0”  X+5 = 0, x = -5
  6. 6. Solving by complete the square  Completing the square is used when the equations doesn’t have a “c” value  Having: x2 + 4x + 1 = 0  The equation cannot be factorizing therefore is necesarry complet the square
  7. 7.  Step 1: Passing to the other side the “c” value x2 + 4x = -1  Step 2: Using the formula (B/2)2 obtain the real “c” value (4/2)2 = 4  Step 3 : Sum the “c” value to both sides of the equation. x2 + 4x + 4 = -1+ 4  Step 4: Factorize the trinomial equation (x+2)2 = 3  Solve the quation by square root
  8. 8. Solving by the quadratic formula  In order to solve difficult equations, quadratic formula is used:  It is used by substituting each value: a, b and c according to the equation given.
  9. 9. *Completing the Square (Completing the Square) http://www.mathsisfun.com/algebra/completing-square.html *Quadratic equations. (2000, January 1). . Retrieved May 29, 2014, from http://mathworld.wolfram.com/QuadraticEquation.html

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