What number needs to be added to both sides of the equation to complete the square? x^2-7x=5

add 5

0

Step-by-step explanation:

Add

5

to both sides of the equation.

x

2

+

7

x

=

5

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

, the coefficient of

x

.

(

b

2

)

2

=

(

7

2

)

2

Add the term to each side of the equation.

x

2

+

7

x

+

(

7

2

)

2

=

5

+

(

7

2

)

2

Simplify the equation.

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x

2

+

7

x

+

49

4

=

69

4

Factor the perfect trinomial square into

(

x

+

7

2

)

2

.

(

x

+

7

2

)

2

=

69

4

Solve the equation for

x

.

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x

=

±

√

69

2

-

7

2

The result can be shown in multiple forms.

Exact Form:

x

=

±

√

69

2

-

7

2

Decimal Form:

x

=

0.65331193

...

,

-

7.65331193

...