# Math

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solve for X 30y=x^2-14x+13

• Math -

x^2 - 14 x + 13 = 30 y
x^2 - 14 x = 30 y - 13
x^2 - 14 x + 49 = 30 y + 36
(x-7)^2 = 30 y + 36
x - 7 = +/- sqrt (30 y + 36)
x = 7 +/- sqrt (30 y + 36)

• Math -

This is so much harder than your other question that I suspect a typo by the way.

• Math -

x^2 - 14 x + 13 = 30 y
x^2 - 14 x = 30 y - 13
x^2 - 14 x + 49 = 30 y + 36 ****
(x-7)^2 = 30 y + 36
x - 7 = +/- sqrt (30 y + 36)
x = 7 +/- sqrt (30 y + 36)

where did you get the 49 or 36

• Math -

Completing the square
x^2 + a x = something
x^2 + a x + (a/2)^2 = something + (a/2)^2
so
if
x^2 -14 x = something
then
x^2 - 14 x +(14/2)^2 = something + (14/2)^2
or
x^2 - 14 x + 49 = something + 49
(x-7)^2 = something + 49
x - 7 = +/- sqrt (something + 49)

by taking half the second coefficient and squaring it, I get a perfect square.

• Math -

and 49 - 13 = 36

• Math -

why is this not correct

30y = x^2 - 14x + 13
- 13
30y - 13 = x^2 - 14x
_________ ___________
-14 -14

x = sqrt 30y-13
_______
-14

Im really trying to follow your work... This is what I got the first time I tried before i asked...

• Math -

sorry the division signs didn't line up correctly