Algebra help: Solve the equation by completing the square?

Question

the problem is this:

Solve the equation by completing the square(^2=2 squared)

4x^2-12x+1=3 ,the answer that i got is x= plus or minus sqrt11 over 2 +1.5, is that correct?

Answer 1

4x^2-12x+1=3, move 1 to other side

4x^2-12x =2, factor out 4 from left

4(x^2 - 3x) = 2, complete the square

4(x^2 - 3x + (3/2)^2) = 2 + 4*(3/2)^2 , note you add same thing to both sides


4(x - 3/2)^2 = 2 + 4*(3/2)^2 , clean things up

4(x - 3/2)^2 = 2 + 4*9/4

4(x - 3/2)^2 = 2 + 9

4(x - 3/2)^2 = 11, div by 4

(x - 3/2)^2 = 11/4, take sqrt

+- (x-3/2) = sqrt(11/4), not sqrt(u^2) = +- u

+- (x-3/2) = sqrt(11)/2

+(x-3/2) = sqrt(11)/2 | - (x-3/2) = sqrt(11)/2

x = (3/2) + sqrt(11)/2 | -x + 3/2 = sqrt(11)/2
| -x = sqrt(11)/2 - 3/2
| x = - sqrt(11)/2 + 3/2

Answer 2

4 x ² - 12 x - 2 = 0
2 x ² - 6 x - 1 = 0
2 (x ² - 3 x - 1/2) = 0
(x ² - 3x + 9/4) - 9/4 - 1/2 = 0
(x - 3/2) ² = 11/4
(x - 3/2) = ± (1/2)√11
x = 3/2 ± (1/2)√11 (we agree!)

Answer 3

yes.

this equation is equivalent to 4x^2-12x-2=0
add 11 to both sides gives
4x^2-12x+9=11
4x^2-12x+9 is equivalent to (2x-3)(2x-3) or (2x-3)^2
so 2x-3=plus or minus sqrt 11
so 2x = (plus or minus sqrt of 11) + 3
so x=((plus or minus sqrt of 11)/2) + 1.5

Answer 4

4x*-12x+1=3
4x*-12x=2
x*-3x=2/4 (3/2)*=9/4
x*-3x+9/4=2/4+9/4
(x-3/2)*=11/4
x-3/2=+-(sqrt 11)/2
x=3/2+-(sqrt 11)/2
You are correct

Answer 5

Rewrite it into time-honored style ... 16x^2 - 7x + a million = 0 Nowhere does the line pass the x axis so this equation has 2 unreal roots. those are (-0.219,0.121) and (0.219,0.121)