1.) 7+7/9x=−42 2.) 4x+1=−15 3.)−4(x−3)=−40
2 answers:
Answer:
1) x= -1/27
2) x=-4
3) x=13
Step-by-step explanation:
1) 7+7/9x= = -42
14/9x= = -42
14/9x X 9x= -42 X 9x
14= -378x
-378x= 14
-378x/-378= 14/-378
x= -1/27
2) 4x+1=−15
4x+1-1=-15-1
4x=-16
4x/4= -16/4
x=-4
3) −4(x−3)=−40
-4(x-3)/-4= -40/4
x-3=10
x-3+3=10+3
x=13
(x2+
7
3 x−
17
3 )=3(x2+
7
3 x+
49
36 −
49
36 −
17
3 ) : x=−
7+√253
6 , x=
√253−7
6 (Decimal: x=−3.81766…, x=1.48432…)
(x2+
7
3 x−
17
3 )=3(x2+
7
3 x+
49
36 −
49
36 −
17
3 )
Expand 3(x2+
7
3 x+
49
36 −
49
36 −
17
3 ): 3x2+7x−17
x2+
7
3 x−
17
3 =3x2+7x−17
Add 17 to both sides
x2+
7
3 x−
17
3 +17=3x2+7x−17+17
Simplify
34
3 +
7
3 x+x2=3x2+7x
Subtract 7x from both sides
34
3 +
7
3 x+x2−7x=3x2+7x−7x
Simplify
x2−
14
3 x+
34
3 =3x2
Subtract 3x2 from both sides
x2−
14
3 x+
34
3 −3x2=3x2−3x2
Simplify
−2x2−
14x
3 +
34
3 =0
Solve with the quadratic formula
x1, 2=
−(−
14
3 )±√(−
14
3 )2−4(−2)
34
3
2(−2)
√(−
14
3 )2−4(−2)
34
3 =
2√253
3
x1, 2=
−(−
14
3 )±
2√253
3
2(−2)
Separate the solutions
x1=
−(−
14
3 )+
2√253
3
2(−2) , x2=
−(−
14
3 )−
2√253
3
2(−2)
x=
−(−
14
3 )+
2√253
3
2(−2) : −
7+√253
6
x=
−(−
14
3 )−
2√253
3
2(−2) :
√253−7
6
The solutions to the quadratic equation are:
X= — 7+/253. /253 — 7
______________ ,x = __________
6 6
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