Question

escreva as equações na forma ax² + bx + c = 0 e identifique os valores de a, b e c:

a) 5+x = 2x + 3x²
b) x² + 7 = 4 - 2x
c) 4x² + 3x = 7 - 3x
d) 3x - 2x = 2 (x-1)
e) x (x-2) = 3(x+6)
f) 5x + 3x² = 4x - 7
g) x² + 4x = 2 (x-1)
h) x (2x-3) = 4x - 1
i) 4x (x+3) + 9 = 0
j) x (x-2) + 1 = (x+3)

Answer 1

$a) 5+x = 2x + 3x^2\to \\\\5+x -3 x^{2} -2x=0\to \\\\ -3 x^{2} -x+5=0\\\\\\ a=-3;b=-1;c=5$




$b) b) x^{2} + 7 = 4 - 2x\to \\\\ x^{2} + 7 -4 + 2x=0\to \\\\ x^{2} + 2x+3=0 \\\\\\ a=1;b=2;c=3$




$c) c) 4 x^{2} + 3x = 7 - 3x\to\\\\ 4 x^{2} + 3x -7 + 3x=0\to\\\\ 4 x^{2} +6x-7=0\to \\\\\\ a=4;b=6;c=-7$




$d) 3x - x^{2} = -5 x^{2} + 8x\to \\\\ 3x - x^{2} +5 x^{2} - 8x=0\to\\\\ 4 x^{2} -5x=0\to\\\\\\a=4;b=-5;c=0$




$e) x (x-2) = 3(x+6)\to \\\\ x^{2} -2x=3x+18\to \\\\ x^{2} -2x-3x-18=0\to \\\\ x^{2} -5x-18=0\\\\\\ a=1;b=-5;c=-18$




$f) 5x + 3 x^{2} = 4x - 7\to \\\\ 5x + 3x^2 - 4x +7=0\to \\\\ 3 x^{2} +x+7=0\\\\\\ a=3;b=1;c=7$



$g) x^{2} + 4x = 2 (x-1)\to\\\\ x^{2} + 4x = 2x-2\to \\\\ x^{2} + 4x - 2x+2=0\to \\\\ x^{2} + 2x+2=0\\\\\\ a=1;b=2;c=2$




$h) x (2x-3) = 4x - 1\to \\\\ 2x^2-3x = 4x - 1\to \\\\ 2x^2-3x-4x + 1=0\to \\\\ 2 x^{2} -7x+1=0\\\\\\ a=2;b=-7;c=1$




$i) 4x (x+3) + 9 = 0\to \\\\ 4 x^{2} +12x+9=0\\\\\\ a=4;b=12;c=9$




$j) x (x-2) + 1 = (x+3)\to \\\\ x^{2} -2x+1=x+3\to \\\\ x^{2} -2x+1-x-3=0\to \\\\ x^{2} -3x-2=0\\\\\\ a=1;b=-3;c=-2$

Answer 2

a)
5 + x = 2x + 3x²
5 + x - 2x - 3x² = 0

R.:
- 3x² - x + 5 = 0
a = - 3; b = - 1; c = 5
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b)
x² + 7 = 4 - 2x
x² + 7 - 4 + 2x = 0
x² + 3 + 2x = 0

R.:
x² + 2x + 3 = 0
a = 1; b = 2; c = 3
*************************
c)
4x² + 3x = 7 - 3x
4x² + 3x - 7 + 3x = 0

R.:
4x² + 6x - 7 = 0
a = 4; b = 6; c = - 7
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d)  Conforme indicado:

3x - x² = - 5x² + 8x
- x² + 5x² + 3x - 8x = 0
R.:
4x² - 5x = 0
a = 4; b = - 5; c = 0

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e)
x (x - 2) = 3(x + 6)
x² - 2x = 3x + 18
x² - 2x - 3x - 18 = 0

R.:
x² - 5x - 18 = 0
a = 1; b = - 5; c = - 18
**************************************
f)
5x + 3x² = 4x - 7
3x² + 5x - 4x + 7 = 0

R.:
3x² + x + 7 = 0
a = 3; b = 1; c = 7
***************************
g)
x² + 4x = 2 (x - 1)
x² + 4x = 2x - 2
x² + 4x - 2x + 2 = 0

x² + 2x + 2 = 0
a = 1; b = 2; c = 2
****************************
h)
x (2x - 3) = 4x - 1
2x² - 3x = 4x - 1
2x² - 3x - 4x + 1 = 0

R.:
2x² - 7x + 1 = 0
a = 2; b = - 7; c = 1
******************************
i)
4x (x + 3) + 9 = 0

R.: 
4x² + 12x + 9 = 0
a = 4; b = 12; c = 9
********************************
j)
x (x - 2) + 1 = (x + 3)
x² - 2x + 1 = x + 3
x² - 2x - x + 1 - 3 = 0

R.:
x² - 3x - 2 = 0
a = 1; b = - 3; c = - 2
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