## x^2+3x-2=0 Solve for x completing the square

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
pistolpete
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### x^2+3x-2=0 Solve for x completing the square

x^2+3x-2=0

I have to solve for x by completing the square

I am a bit slow and get stuck at this part:
x^2+3x-2=0
x^2+3x=2
x^2+3x+2.25=4.25
(x+ )(x+ )=4.25

I can't factor the 2.25 to get 3. Or am i doing this wrong???

pistolpete
Posts: 13
Joined: Wed May 20, 2009 1:07 am
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### Re: x^2+3x-2=0 Solve for x completing the square

nevermind i got it thanks..

stapel_eliz
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x^2+3x-2=0

I have to solve for x by completing the square

To complete the square to solve this quadratic, the steps are as follows:

. . . . .$x^2\, +\, 3x\, -\, 2\, =\, 0$

. . . . .$x^2\, +\, 3x\, =\, 2$

Take half of +3, square it, and add to both sides:

. . . . .$x^2\, +\, 3x\, +\, \frac{9}{4}\, =\, 2\, +\, \frac{9}{4}$

Convert the left-hand side, using the +3/2, to perfect-square form:

. . . . .$\left(x\, +\, \frac{3}{2}\right)^2\, =\, \frac{8}{4}\, +\, \frac{9}{4}$

. . . . .$\left(x\, +\, \frac{3}{2}\right)^2\, =\, \frac{17}{4}$

. . . . .$x\, +\, \frac{3}{2}\, =\, \pm \frac{\sqrt{17}}{2}$

...and so forth.

pistolpete
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### Re: x^2+3x-2=0 Solve for x completing the square

I did it by the use of decimals.

x^2+3x+2.25=4.25
(x+1.5) (x+1.5)=4.25
(x+1.5)^2=4.25

sqgrt both sides

x+1.5=sgrt(4.25)
-1.5 -1.5

x= -1.5 +-sgrt(4.25)

is this correct also?

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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If you are allowed to format the answers using decimals, then yes, your answer is "right". But most books and instructors don't like the decimal form, even though the value is exactly the same.

Check with your instructor to be sure.