completing the square

Shoppingal

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Sep 28, 2011
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x^2 -5 = 3x -10
x^2 -5 -3x +10 = 0
x^2 - 3x +5 = 0
(x^2 - 3/2x) + 5 = 0
(x^2 - 3/2x + 9/16 - 9/16) + 5 = 0
(x^2 - 3/2x + 9/16) - 9/16 +5 = 0
(x - 3/4)^2 + 4 7/16 = 0

Have I done this correctly?
 
x^2 -5 = 3x -10
x^2 -5 -3x +10 = 0
x^2 - 3x +5 = 0
(x^2 - 3/2x) + 5 = 0
(x^2 - 3/2x + 9/16 - 9/16) + 5 = 0
(x^2 - 3/2x + 9/16) - 9/16 +5 = 0
(x - 3/4)^2 + 4 7/16 = 0

Have I done this correctly?

Yes
 
x^2 -5 = 3x -10
x^2 -5 -3x +10 = 0
x^2 - 3x +5 = 0
(x^2 - 3/2x) + 5 = 0
(x^2 - 3/2x + 9/16 - 9/16) + 5 = 0
(x^2 - 3/2x + 9/16) - 9/16 +5 = 0
(x - 3/4)^2 + 4 7/16 = 0

Have I done this correctly?

No.

The solutions to (x - 3/4)^2 + 4 + 7/16 = 0 are:

\(\displaystyle x = \frac{3}{4} \pm \frac{1}{4} \sqrt{71} \cdot i\)

The solutions to x^2 -5 = 3x -10 are different.

The first three lines of your work are good.

PS: In algebra, we do not generally convert improper fractions to mixed numbers, like 4 7/16. Just leave them as improper fractions.
 
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