Makakuha ng detalyadong mga sagot sa iyong mga tanong gamit ang IDNStudy.com. Ang aming platform ay nagbibigay ng mga maaasahang sagot upang matulungan kang gumawa ng matalinong desisyon nang mabilis at madali.
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.