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6 April, 18:22

X^2-4x-3=0

solve by using completing the square

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Answers (1)
  1. 6 April, 19:15
    0
    Answer:3,1

    Step-by-step explanation:Subtract

    3

    3

    from both sides of the equation.

    x

    2

    -

    4

    x

    =

    -

    3

    x

    2

    -

    4

    x

    =

    -

    3

    To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of

    b

    b

    .

    (

    b

    2

    )

    2

    =

    (

    -

    2

    )

    2

    (

    b

    2

    )

    2

    =

    (

    -

    2

    )

    2

    Add the term to each side of the equation.

    x

    2

    -

    4

    x

    +

    (

    -

    2

    )

    2

    =

    -

    3

    +

    (

    -

    2

    )

    2

    x

    2

    -

    4

    x

    +

    (

    -

    2

    )

    2

    =

    -

    3

    +

    (

    -

    2

    )

    2

    Simplify the equation.

    Tap for fewer steps ...

    Raise

    -

    2

    -

    2

    to the power of

    2

    2

    .

    x

    2

    -

    4

    x

    +

    4

    =

    -

    3

    +

    (

    -

    2

    )

    2

    x

    2

    -

    4

    x

    +

    4

    =

    -

    3

    +

    (

    -

    2

    )

    2

    Simplify

    -

    3

    +

    (

    -

    2

    )

    2

    -

    3

    +

    (

    -

    2

    )

    2

    .

    Tap for fewer steps ...

    Raise

    -

    2

    -

    2

    to the power of

    2

    2

    .

    x

    2

    -

    4

    x

    +

    4

    =

    -

    3

    +

    4

    x

    2

    -

    4

    x

    +

    4

    =

    -

    3

    +

    4

    Add

    -

    3

    -

    3

    and

    4

    4

    .

    x

    2

    -

    4

    x

    +

    4

    =

    1

    x

    2

    -

    4

    x

    +

    4

    =

    1

    Factor the perfect trinomial square into

    (

    x

    -

    2

    )

    2

    (

    x

    -

    2

    )

    2

    .

    (

    x

    -

    2

    )

    2

    =

    1

    (

    x

    -

    2

    )

    2

    =

    1

    Solve the equation for

    x

    x

    .

    Tap for fewer steps ...

    Take the

    square

    square

    root of each side of the

    equation

    equation

    to set up the solution for

    x

    x

    (

    x

    -

    2

    )

    2



    1

    2

    =

    ±



    1

    (

    x

    -

    2

    )

    2



    1

    2

    =

    ±

    1

    Remove the perfect root factor

    x

    -

    2

    x

    -

    2

    under the radical to solve for

    x

    x

    .

    x

    -

    2

    =

    ±



    1

    x

    -

    2

    =

    ±

    1

    Any root of

    1

    1

    is

    1

    1

    .

    x

    -

    2

    =

    ±

    1

    x

    -

    2

    =

    ±

    1

    The complete solution is the result of both the positive and negative portions of the solution.

    Tap for fewer steps ...

    First, use the positive value of the

    ±

    ±

    to find the first solution.

    x

    -

    2

    =

    1

    x

    -

    2

    =

    1

    Move all terms not containing

    x

    x

    to the right side of the equation.

    Tap for fewer steps ...

    Add

    2

    2

    to both sides of the equation.

    x

    =

    1

    +

    2

    x

    =

    1

    +

    2

    Add

    1

    1

    and

    2

    2

    .

    x

    =

    3

    x

    =

    3

    Next, use the negative value of the

    ±

    ±

    to find the second solution.

    x

    -

    2

    =

    -

    1

    x

    -

    2

    =

    -

    1

    Move all terms not containing

    x

    x

    to the right side of the equation.

    Tap for fewer steps ...

    Add

    2

    2

    to both sides of the equation.

    x

    =

    -

    1

    +

    2

    x

    =

    -

    1

    +

    2

    Add

    -

    1

    -

    1

    and

    2

    2

    .

    x

    =

    1

    x

    =

    1

    The complete solution is the result of both the positive and negative portions of the solution.

    x

    =

    3

    ,

    1

    x

    =

    3

    ,

    1
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