Math Question?

Question

Hey.. i am kinda stuck on this math question..
1/2x^2+x-1=0

im supposed to use, the completing the square method.. .can anyone help

oh yeah, im supposed to solve exactly.

Answer 1

Start by multiplying everything by 2, to get to a 1 as a coefficient on the x² term:
x² + 2x - 2 = 0

Now put the 2 on the right hand side (subtract 2 from both sides):
x² + 2x = 2

Now complete the square by taking half of the x coefficient (2/2 = 1) and squaring it (1² = 1). Add this to both sides:

x² + 2x + 1 = 2 + 1

Now write this as a square:
(x + 1)² = 3

Take the square root and you have:
x + 1 = ± sqrt(3)

Subtract 1 from both sides and you have x:
x = -1 ± sqrt(3)

Answer 2

-2/3 because 1/2x^2+x-1=0. Subtract the 1 from the 2 on the left side and u end up with 1/2x+1+x=0. Then u add the x to the 1/2x and get 1 1/2. Then u subtract 1 from both sides and get 1 1 1/2x= -1.Then u divide 1 1/2x from both sides and get x= -2/3

Answer 3

x = +/- sqrt( (-4(1/2)(-1))/1 ), simplified to...

x = -1 +/- 1/sqrt (3)

x= .7320508076 or -2.7320508076 (this part is right for sure -- solved using solver function on TI-89)

Answer 4

(1/2x)² + x - 1 = 0
(1)² - 4.1/2.-1
1 + 2 = 3
x = (-1 +/-\/3) : 2.1/2
x' = (-1 + \/3) : 1 = -1 + \/3
x" = -1 - \/3
Solution: {x = -1 + \/3 or x = -1 - \/3}
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Answer 5

x^2+2x-2=0
x^2+2x+1-3=0
(x+1)^2-3=0
(x+1)^2=3
x+1=+-Sqrt[3]
x=-1+-Sqrt[3]

Answer 6

use the quadratric equation.