completing the square to solve 5 + 2x^2 = -6x

[humakhan]

5 + 2x^2 = -6x

The instructions say to solve by completing the square. I did the following:

2x^2 + 5 + 6x = 0
5 + 7x^2 = 0
x^2 + 1/7 + 5/7 = 0
5/7 + x^2 = 1/7
so then offcourse
x^2 = 1/7 - 5/7
x^2 = -4/7

I think I maybe did this wrong. I did it by the book, but maybe this method isn't right for this problem...?

 

[tkhunny]

1) 2x^2 + 5 + 6x = 0
2) 5 + 7x^2 = 0

How did you get from 1) to 2)?

Careful and deliberate.

5 + 2x^2 = -6x

Rearrange

2x^2 + 6x = -5

Divide by 2

x^2 + 3x = -5/2

Calculate the magic number you need to complete the square.

3/2 = 3/2
(3/2)^2 = 9/4

Add 9/4

x^2 + 3x + 9/4 = -5/2 + 9/4

Simplify

(x + 3/2)^2 = -1/4

Oops! We can quite right there. Why?

Look at this problem the way I have done it. I'm not saying you have to copy me exactly, but I AM saying you should develop a style that can be followed, reviewed, checked and understood.

 

[humakhan]

this is a bit confusing..but hopefully when i keep trying out these kinds of problems i'll get it right

 

[tkhunny]

ALL we are doing is exploiting this: (a+b)^2 = a^2 + 2ab = b^2

You didn't answer my question.

 

[humakhan]

ok
but can't you do this...
(x + 3/2)^2 = - 1/4
x^2 + 3/4 = - 1/4
x^2 = -1/4 - 3/4
x^2 = -1....

 

[stapel]

can't you do this...
(x + 3/2)^2 = - 1/4
x^2 + 3/4 = - 1/4

How did you go from "(x + 3/2)²" to "x² + 3/4"?

Please reply showing your steps. Thank you.

Eliz.

 

[tkhunny]

(Real Number)^{2}

Ask yourself, "Can that be negative?"

Any way you manipulate it, if you get a different result, something went wrong.

Thinking is more effective than ploughing.