FOr only the people who are really good and experienced at math?

Question

Solve by completing the square...

2x^2 - 7x + 1 = 0

show your work

don't use the quadratic formula, solve by completing the square

Answer 1

2(x^2-7x/2+1/2)=0
2((x-7/4)^2-49/16+1/2)=0
2(x-7/4)^2-41/8=0
(x-7/4)^2=41/16
x-7/4=±√41/4
x=(7±√41)/4

Answer 2

You want an expression like (ax+b)^2 to come out 2x^2 - 7x + z;
This must be like (x*√2 - b)^2, which when expanded is 2x^2 - 2√2bx + b^2. The middle term must be -7x, so 2√2*b = 7, so b = 7/(2√2). The binomial squared becomes (x√2 - 7/2√2)^2 = 2x^2 - 7x + 49/8; The difference between this and the expression you were given is 1-49/8; add that to the expression you have and you will "complete the square" to get (x√2 - 7/2√2)^ + 1 - 49/8; when you expand the square of the binomial, the last term will be 49/8, which will cancel with the -49/8, leaving the 1. So your equation is now

(x√2-7/2√2)^2 = 49/8-1; take the square root of both sides:

x√2 - 7/2√2 = ±√(49/8-1)

x√2 = 7/2√2 ± √(49/8-1)

x = 7/4 ± √[(49/8-1)/2]

Answer 3

2x^2 - 7x + 1 = 0
x^2 - 7/2x + 1/2 = 0
equation of the form a^2 + 2ab + b^2 = 0 => (a + b)^2 =0
to generate the perfect square 2ab = -7/2 and a=1 so b = -7/4
then we have to add (-7/4)^2 to both sides of the equation
x^2 - 7/2 x +(-7/4)^2 = (-7/4)^2 - 1/2
(x - 7/4)^2 = 49/16 - 1/2 = 41/16
the solution will be:
x - 7/4 = +/- sqrt(41/16)
x will have 2 solutions:
x = 7/4 + sqrt(41)/4 or x = 7/4 - sqrt(41)/4

Answer 4

2x^2 - 7x + 1 = 0
x^2 - (7/2)x + 1/2 = 0
x^2 - (7/2)x + (7/4)^2 -(7/4)^2 = -1/2
(x - (7/4))^2 = -1/2 + 49/16
(x - 7/4) = ±sqrt(49/16 - 8/16)
x = (7 ± sqrt(41))/4
x = ( 0.14922, 3.35078)

Answer 5

2x^2-7x+1=0
x^2-7x/2+1/2=0
x^2-7x/2 = -1/2
x^2-7x/2+49/16=-1/2+49/16
(x-7/4)^2=41/16
x-7/4=+-sqrt(41/16)
x=7/4+-sqrt(41/16)
x=1/4(7+-sqrt(41))

Answer 6

x= (7 + √41)/14
and
x= (7 - √41)/14

Answer 7

(√2*x - 7/(2√2))^2 - (7/(2√2))^2 + 1 = 0

(√2*x - 7/(2√2))^2 = + (7/(2√2))^2 - 1

etc etc.

Answer 8

by formula -b+- root( ( b^2-4ac))/2a
7+root ((49-8))/4
( 7+6.41)4
= 3.3525
- 059/4
0 .1475

x= 3.3525 or 0.1475