SOLUTION: how do i solve 12 x � +19 x=21 by completing the square and using the formula a(x-h)�+k

Question 308383: how do i solve 12 x � +19 x=21 by completing the square and using the formula a(x-h)�+k
Found 2 solutions by Fombitz, CharlesG2:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Factor out the 12 from the left hand side,

Take (1/2) of the x-coefficient and square it.
Add it to both sides (remember to multiply by 12 for the right hand side).

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.
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The vertex occurs at
(-19/24,-1369/48)or approximately (-0.8,-28.5)
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
how do i solve 12 x � +19 x=21 by completing the square and
using the formula a(x-h)�+k
a(x-h)^2 + k = a(x^2 - 2hx + h^2) + k = 0
12x^2 + 19x - 21 = 0
12(x^2 + (19/12)x - (21/12)) = 0
12(x^2 + (19/12)x + (19/24)^2 - (21/12)) = 12(19/24)^2
12(x + (19/24))^2 + 12(-21/12) = 12(19/24)^2
12(x + (19/24))^2 - 21 - 12(361/576) = 0
-21 - 12(361/576) = -21 - 4332/576 = -12096/576 - 4332/576 = -16428/576
-16428/576 = -1369/48 = -28 and ?/48
-28 * 48 = -1344
-1369/48 = -28 and 25/48 = approx. -28.52083
12(x + (19/24))^2 - 1369/48 = 0 [a(x-h)^2 + k = 0 form]
h = - 19/24 = approx. -0.79167
k = -1369/48 = approx. -28.52083
(h,k) is the vertex of this parabola which opens upward since a = positive 12
(x + (19/24))^2 = 1369/48 * 1/12
(x + (19/24))^2 = 1369/576
x + 19/24 = 37/24 OR x + 19/24 = -37/24
x = 18/24 = 3/4 OR x = -56/24 = -7/3

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