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