Solve the equation 1/2x ^2 - 11/2x + 15 = 0 by completing the square.?

Question

Solve the equation 1/2x ^2 - 11/2x + 15 = 0 by completing the square.

a. x = -1 ± 5 √6
b. x = 5 or 6
c. x = -5 or -6
d. x = 11/2or 12
e. x = 1/2 or -1

Answer 1

(1/2) x^2 - (11/2) (x) + 15 = 0
multiply by 2
x^2 - 11x + 30 = 0
(x)^2 - 2(1) (11/2) x + (11/2)^2 - (11/2)^2 + 30 = 0
(x)^2 - 2(1) (11/2) x + (11/2)^2 - (121/4) + 30 = 0
(x- 11/2)^2 = 121/4 - 30
(x - 11/2)^2 = 1/4 = (1/2)^2
x - 11/2 = +1/2 or - 1/2
x = 11/2 + 1/2 or 11/2 - 1/2
6 or 5

Answer 2

(1/2)x ^2 - (11/2)x + 15 = 0

First, multiply both sides by 2 to get rid of fraction.

x^2 - 11x + 30 = 0
x^2 - 11x = -30

take the 11, divide it by two, then square it. Add that to both sides.

x^2 - 11x + (11/2)^2 = -30 + (11/2)^2
(x - 11/2)^2 = -30 + 121 / 4
(x - 11/2)^2 = -120/4 + 121/4
(x - 11/2)^2 = 1/4

take square root of both sides
x - 11/2 = +- 1/2
x = 11/2 +- 1/2
x = (11/2 - 1/2) AND (11/2 + 1/2)
x = (10/2) AND (12/2)
x = 5 AND 6

Answer 3

The quadratic equation "general solution" is based on completing the square, so it doesn't make sense to reinvent the wheel. So.....
x = 11/2 +/- sqrt([121/4]-4*1/2*15)
x = 11/2 +/- 1/2 , x= 5 or 6 (b)

Answer 4

1/2x ^2 - 11/2x + 15 = 0
x ^2 - 11x + 30 = 0
x ^2 - 2*x*(11/2) + (11/2)^2 + 30 - (11/2)^2= 0
(x - 11/2)^2 = (11/2)^2 - 30
(x - 11/2)^2 = 121/4 - 30
(x - 11/2)^2 = 1/4
(x - 11/2) = ± 1/2
x = 11/2 ± 1/2
x = 6, 5

Answer 5

1/2 x^2 - 11/2 x + 15 = 0
x^2 - 11x + 30 = 0 (* eq by 2)
x^2 - 11x = -30
x^2 - 11x + (11/2)^2 = (11/2)^2 - 30
(x - 11/2) ^ 2 = 121/4 - 120/4 = 1/4
(x - 11/2) = +1/2 or -1/2
x = 11/2 + 1/2 = 6 or 11/2-1/2 = 5

Ans is b

Answer 6

1/2x^2-11/2x+15=0
multiply both sides by 2;
x^2-11x+30=0
[(x-11/2)^2+30-121/4]=0
(x-11/2)^2+(120-121)/4=0
(x-11/2)^2=1/4
take sq. roots of two sides;
x-11/2= +/- 1/2
x=11/2+/- 1/2
=6,5ANS.

Answer 7

b. x=5 or 5