complete the square 2x²+5x-3=f(x)?

Question

steps in completeing the square for this equation?

Answer 1

f(x) = 2(x² + 5/2 x - 3/2)
f(x) = 2(x² + 5/2 x + 25/16 - 25/16 - 3/2)
f(x) = 2 [ (x² + 5/2 x + 25/16) - 49/16 ]
f(x) = 2 [ (x + 5/4)² - (7/4)² ]

Answer 2

completing the square: x^2 + bx + (b/2)^2 = (x + b/2)^2

f(x) = 2x^2 + 5x - 3
= 2(x^2 + 5/2 x) - 3
= 2(x^2 + 5/2 x + (5/4)^2 - (5/4)^2) - 3
= 2(x^2 + 5/2 x + (5/4)^2) - 2(5/4)^2 - 3
= 2(x + 5/4)^2 - 2(25/16) - 3
= 2(x + 5/4)^2 - 25/8 - 24/8
= 2(x + 5/4)^2 - 49/8

alternate method:

let y = f(x), and put right hand side in the form x^2 + bx:

y = 2x^2 + 5x - 3
y + 3 = 2x^2 + 5x
(y + 3)/2 = x^2 + 5/2 x

now add (b/2)^2 to both sides to complete the square on the right:

(y + 3)/2 + (5/4)^2 = x^2 + 5/2 x + (5/4)^2
(y + 3)/2 + 25/16 = (x + 5/4)^2

now solve for y:

(y + 3)/2 = (x + 5/4)^2 - 25/16
y + 3 = 2(x + 5/4)^2 - 2(25/16)
y = 2(x + 5/4)^2 - 25/8 - 3
y = 2(x + 5/4)^2 - 49/8
f(x) = 2(x + 5/4)^2 - 49/8

Answer 3

step 1. reduce the equation so that the second degree power will have 1 as its coefficient...x^2+(5/2)x-3/2=0
step 2. get the 1/2 of the coefficient of the x (1 as exponent) and then square it. (5/2 * 1/2)^2 =(5/4)^2= 25/16
step 3. add the quantity obtained in step 2,but subtract the same quantity so that no effect is given in the equation,that is, x^2+(5/2)x-3/2 + 25/16 - 25/16 =0
step 3. regroup x^2+(5/2)x +25/15 -3/2 -25/16, then
x^2+(5/2)x +25/15(which is a perfect square) --49/16 is equal to (x+5/4)^2-49/16=0(final answer)

Answer 4

f(x) = 2x² + 5x - 3

fisrt, take out the 2
f(x) = 2(x² + (5/2)x - 3)

saparate the x's
f(x) = 2[ (x² + (5/2)x) - 3]

now add (b/2)^2 for both sides. What you do on one side, you need the same thing on the other side.
Notice that you add (b/2)^2 inside the brackets. the (x² + (5/2)x) - 3 are militplied by 2, so you need to add 2(b/2)^2 on the left side

so
f(x) + 2[ (5/2)/2]^2 = 2[(x² + (5/2)x + ((5/2)/2)^2) - 3]

simplfy
f(x) + 25/8 = 2[x² + (5/2)x + 25/16] - 3

factor and subtract 25/8 for both sides
f(x) = 2(x + 5/4)^2 - 49/8 <== answer

hope it helps
Rec

Answer 5

2x²+5x=3
2(x²+5/2x+??)=3 <--- take half the middle term and square it
2(x²+5/2x+25/16)=3+50/16
2(x+5/4)²=6 2/16

Answer 6

step 1: 2x^2+5x-3=y
step2:2y^2+5y-3=x
step3:use the method "completing the square"
and it will look like this:
(2y-1)(y+3)=0
step4:
2y-1-0 y+3=0
y=1/2 y=-3
so your solution set is:
Ss{1/2} and Ss{3}

Answer 7

lol i can't its to late but ask me anothe one tomarrow sometime...............lol