x²-6x+____. Comlplete the square??

Question

1) x²-6x+___. Complete the sq.

2) x²-6x=16 Solve by completing the square

3) 2x²-3x+1=0

Answer 1

1)
(x-3)² = x²-6x+9
You can get that 3 from 0.5 × 6. It's always 0.5

2)
(x-3)²+n=16
<=> x²-6x+9+n=16
<=> x²-6x+9-9=16
(x-3)²-9=16
(x-3)²=16+9
(x-3)²=25
x-3 = ± sqrt (25)
x-3 = ± 5

x-3 = 5
x=8

or

x-3 = -5
x=-2

3)
2x²-3x+1=0
2(x²-1.5x+.5)=0
2((x-0.75)²+n)=0
2((x-0.75)²-1/16)=0
(x-0.75)²-1/16=0
(x-0.75)²=1/16
x-0.75=±1/4

x = 1/4 + 3/4
x = 1

or

x = -1/4 + 3/4
x = 1/2

Answer 2

to complete the square, take the coefficient of x (b in the quadratic), divide it by 2, and then square it and add that to both sided of the equation


# 2

x² - 6x = 16
b = 6; dived by 2 and square it
(6/2)² = 9
so add 9 to both sides
x² - 6x -16 = 0
x² - 6x + 9 - 16 = 9
(x-3)(x-3) -16 = 9
(x-3)² = 9 + 16
(x-3)² = 25
x -3 = + or - square root of 25
x -3 = + or - 5
x - 3 = 5
x = 8
x - 3 = -5
x = -2

so x = 8 and x = -2

3
2x² - 3x + 1 = 0
divide everything by 2
x² - 3/2x + 1/2 = 0
x² - (3/2)x + 9/16 + 1/2 = 9/16
(x² - (3/2)x + (9/16)) + 1/2 = 9/16
(x² - (3/2)x + (9/16)) = 9/16 - 1/2
(x-3/4)² = 9/16 - 8/16
(x - 3/4)² = 1/16
x - 3/4 = + or - sqr (1/16)
x - 3/4 = + or - 1/4
x - 3/4 = -1/4 and x - 3/4 = 1/4
x = -1/4 + 3/4
x = 1/2
and
x = 1/4 + 3/4
x = 1

x = 1/2 and x = 1

Answer 3

1) x² - 6x + 9

2) x² - 6x = 16
x² - 6x + 9 = 16 + 9
(x - 3)² = 25
x - 3 = ±5
x = 3 ± 5
x = 3 + 5 = 8 or x = 3 - 5 = -2

3) 2x² - 3x + 1 = 0
(2x - 1)(x - 1) = 0
x = 1/2 or x = 1

Answer 4

1) (x-3)^2 -9

2) (x-3)^2 -9 -16 = 0
(x-3)^2 - 25 = 0
(x-3)^2 = 25
(x-3) = 5 (x-3) = -5
x = 8 x = -2

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

Answer 5

1) x²-6x+9= (x-3)²


2) x²-6x+9-9=16
x²-6x+ 9=16+9
(x-3)²=25 /sqrt
x-3=(+-)5
x=3(+-)5
x(1)=3+5
x(1)=8
x(2)=3-5
x(2)=-2



3)2x²-3x+1=0
You can use many methods for solving this like
2x²-2x-x+1=0
2x(x-1)-(x-1)=0
(x-1)(2x-1)=0
now you have two equations
x(1)-1=0 2x(2)-1=0
x(1)=1 x(2)=1/2

Answer 6

You havent really explained it.

Its a quadratic equation.

Answer 7

WHAT THE ****?! ARE YOU KIDDING ME?! Let me ask you a question, trust me, it is as simple as this one. Do you pay attention in class?