help please it's confusing

Question

Solve each of the following by completing the square:

1. 2x²– 8x + 4 = 0
2. 2x²– 9x + 8 = 0

Express each of the following in the form y = a(x – h)²+ k. Hence state the coordinates of the vertex:

1. y = x²+ x
2. y = x²– x
3. y = x²+ 3x + 9

Answer 1

2x^2 -8x +4 =0

divide by 2

x^2 -4x +2 = 0

x^2 -4x +4 = -2+4

(x-2)^2 = 2

x-2 = +/-sqr2

x = 2 +sqr2 or 2-sqr2

x = about 3.414 or 0.586

maybe check the answer by graphing it and seeing if the x intercepts match

it's an upward opening parabola that intersects the x axis twice

y=x^2+x

y = x^2 +x + 1/4 - 1/4

y = (x+1/2)^2 - 1/4

y = (x-h)^2 +k

(h,k) = (-1/2, -1/4)= vertex = minimum

use a graphing calculator, either on line or handheld

or use an online equation calculator

2x^2-9x+8=0

x^2 -9x/2 +4 = 0

x^2 -9x/2 = -4

to complete the square

take the x coefficient (9/2), half it to get (9/4), then square it to get (9/4)^2, then add it to both sides of the equation

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

(x-9/4)^2 = -4 + 81/16 = -64/16 +81/16 = 17/16

x -9/4 = +/-sqr(17/16) = +/-sqr17/4

x = 9/4 +/- .25sqr17

x = 2.25 +/-.25sqr17

x = about 3.28 or 1.22

(calculations get a little tedious, so no guarantees of no errors above, but it's the basic solution method of "completing the square")

x^2 -x is very similar

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

(x- 1/2)^2 = 1/4

x -1/2 = 1/2

x = 1/2 +1/2 = 1

x=1

check the answer

plug 1 into the original equation

x^2-x=0

1^2 -1 =0

1-1=0

x^2+3x +9=0

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

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

x+3/2 = +/-sqr(--36+9)/4)= +/-sqr(-27/4)

x=-3/2 +/-(1/2)sqr-27

= two imaginary numbers

=-1.5 +/- .5isqr27

= 1.5 +/-.5(3)sqr3

=1.5+/-1.5sqr3

=about 4.1 or -1.1

with luck no arithmetic mistakes above