How to answer quadratic Equations? (高手請進)

1.) 2x(2) + 7x=0
X(2X+7)=0
X=0 or 2X+7=0
X= 0 OR 2X= - 7
Ans: X=0 OR X= - 3.5

2.) X(2) - 16=0
X(2) - 4(2)=0
(X-4)(X+4)=0
Ans: X = 4 OR X = - 4

3.) 5x(2)=0
X (2) = 0
X = 0

4.) 3t(2)-12=0
3[t(2) - 4] = 0
t(2) - 2(2) = 0
(t - 2) (t+2) = 0
t=2 or t= -2

5.) (3x(2)-2x)/4=0
X(3X-2) = 0
X=0 or 3X-2 = 0
X=0 or 3X=2
X = 0 or X =3份之2

6.)0= -3w(2)
w=0

7.)halfx(2)+one thirdx=0
3x(2) + 2x=0
x(3x + 2) = 0
x=0 or x = 負3份之2

Solution:

1.2x^2 + 7x = 0
x (2x + 7) = 0
x = 0 or x = -7/2

2.x^2 – 16 = 0
(x – 4) (x + 4) = 0
x = 4 or x = -4

3.5x^2 = 0
x^2 = 0
x = 0

4.3t^2 – 12 = 0
3 (t^2 – 4) = 0
t^2 – 4 = 0
(t – 2) (t + 2) = 0
t = 2 or t = -2

5.(3x(2)-2x)/4=0
3x^2 – 2x = 0 (4)
3x^2 – 2x = 0
x (3x – 2) = 0
x = 0 or x = 2/3

6.0= -3w(2)
3w^2 = 0
w^2 = 0
w = 0

7.1/2(x^2) + (1/3)x = 0
3/6(x^2) + (2/6)x = 0
1/6(3x^2 + 2x) = 0
3x^2 + 2x = 0
x (3x + 2) = 0
x = 0 or x = -2/3