Solving Quadratic Equation by Completing the Square

By sharwell
  • Starting Equation

    Starting Equation

    Equation must be in this form to start solving:
    ax^2+bx+c=0
  • First Step

    First Step

    Move c to the other side
    x^2+6-7=0
    +7 +7
  • Move c to other side

    Move c to other side

    Now:
    x^2+6x=7
  • Divide the b term by 2

    Divide the b term by 2

    b=6
    6/2=3
  • Sqare the b term

    Sqare the b term

    Now:
    b=3^2
    b=9
  • Add that value to both sides

    Add that value to both sides

    x^2+6x(+9)= 7(+9)
  • Create a Perfect Square Trinomial

    Create a Perfect Square Trinomial

    Perfect Square: x^2+6x+9= Perfect Square: 16
  • Factor the left side of equation

    Factor the left side of equation

    =x^2+6x+9
    =(x+3)(x+3)
    =(x+3)^2
  • Square Root both sides

    Square Root both sides

    SR(x+3)^2=SR(16)
    x+3=+/-(4)
  • Add/Subract to find Answers

    Add/Subract to find Answers

    x=3+/-(4)
    x=3+4
    x=7
    x=3-4
    x= -1