Can anyone explain how to answer these quadratic equations by completing the square:?

Question

5x^2+8x-2=0

and 15-6x-2x^2=0

Answer 1

5x^2 + 8x - 2 = 0
5x^2 + 8x = 2
x^2 + (8/5)x = (2/5)
x^2 + (8/5)x + (16/25) = (26/25)
(x + (4/5))^2 = (26/25)
x + (4/5) = sqrt(26/25)
x + (4/5) = ±(1/5)sqrt(26)
x = (-4/5) ± (1/5)sqrt(26)
or
x = (1/5)(-4 ± sqrt(26))
--------------------------------------------

15 - 6x - 2x^2 = 0
-2x^2 - 6x + 15 = 0
-(2x^2 + 6x - 15) = 0
2x^2 + 6x - 15 = 0
2x^2 + 6x = 15
x^2 + 3x = (15/2)
x^2 + 3x + (9/4) = (39/4)
(x + (3/2))^2 = (39/4)
x + (3/2) = sqrt(39/4)
x + (3/2) = (1/2)sqrt(39)
x = (-3/2) ± (1/2)sqrt(39)
or
x = (1/2)(-3 ± sqrt(39))

Answer 2

OK! I will show you the path...

Note: (x+a)^2 = x^2 +2ax + a^2 is the complete square

When we find a non-complete square like x^2 + 2ax .... we must follow the steps:

1) The coeficient of x^2 must be 1. If it is not you divide the equation so that it change to 1
2)Take apart the coeficient of x and divide it by 2. So you get the value of a.
3) Add and subtract a^2 to the equation
4) The three first terms are the complete square (x+a)^2 and you put the other terms to the other side, adding them... it will be a number b.
5) Now you have (x+a)^2 = b and the solutions are:
x+a = sqrt(b) or x+a = -sqrt(b) and finally you got the solutions: x= -a+sqrt(b) or x= -a -sqrt(b)

Let´s do the first for you:

5x^2 + 8x - 2 = 0
1) divide all by 5 x^2 + (8/5)x - 2/5 = 0
2) take the coeficiente 8/5 apart and divide by 2... a=4/5
3) add and subtract 16/25 to the equation
x^2 + (8/5)x + 16/25 - 16/25 -2/5 = 0
4) the first 3 terms are the complete square
(x - 4/5)^2 = 16/25+2/5 add the number in side 2
5) (x-4/5)^2 = 36/25 and x-4/5 = 6/5 or x-4/5 = -6/5
and finally x= 4/5 +6/5 = 2 or x = 4/5 -6/5 = -2/5

Now you work

Answer 3

1) 5x^2 + 8x = 2
x^2 + 8/5 x = 2/5
add (8/10)^2 to each side
(x + 8/10 )^2 = 2/5 + (8/10)^2

solution x+ 8/10 = + or - sqrt(2/5 + (8/10)^2)
solve x now and get the answers

2) same apllies to the other equation

Answer 4

On first one, divide each side by 5, giving you x^2+(8/5)x-(2/5)=0.
Now, to find out what constant value has to be on left side, divide
8/5 by 2, and square it, giving you (8/10)^2 = 64/100.

Now, that means you have to add (64/100)+(2/5) to each side.
So, (64/100)+(2/5) = (64/100)+(40/100) = 104/100.
So, that gives you x^2+(8/5)x+(64/100) = 104/100, or
(x+(8/10))^2 = 104/100.

So, can you do the next one?

Answer 5

2x^2-6x+15
(2x^2+__+15)-6x
Does that help?

Answer 6

It is explained very well here

Answer 7

Cool....contact me.