X^2-4x-3=0

solve by using completing the square

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.

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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

.

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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

.

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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.

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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.

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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.

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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