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what is the answer in
3x(x-2)=7


Sagot :

Answer:

To solve the equation

3

x

(

x

2

)

=

7

3x(x−2)=7, follow these steps:

Distribute

3

x

3x inside the parentheses:

3

x

2

6

x

=

7

3x

2

−6x=7

Move all terms to one side of the equation to set it to zero:

3

x

2

6

x

7

=

0

3x

2

−6x−7=0

Solve the quadratic equation using the quadratic formula,

x

=

b

±

b

2

4

a

c

2

a

x=

2a

−b±

b

2

−4ac

, where

a

=

3

a=3,

b

=

6

b=−6, and

c

=

7

c=−7:

Calculate the discriminant:

Δ

=

b

2

4

a

c

=

(

6

)

2

4

3

(

7

)

=

36

+

84

=

120

Δ=b

2

−4ac=(−6)

2

−4⋅3⋅(−7)=36+84=120

Compute the square root of the discriminant:

120

10.95

120

≈10.95

Apply the quadratic formula:

x

=

(

6

)

±

120

2

3

=

6

±

10.95

6

x=

2⋅3

−(−6)±

120

=

6

6±10.95

Calculate the two solutions:

x

1

=

6

+

10.95

6

16.95

6

2.825

x

1

=

6

6+10.95

6

16.95

≈2.825

x

2

=

6

10.95

6

4.95

6

0.825

x

2

=

6

6−10.95

6

−4.95

≈−0.825

So, the solutions are approximately

x

2.825

x≈2.825 and

x

0.825

x≈−0.825.