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
I did it below after you asked
Here again:
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#
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 - Damon, Wednesday, April 23, 2008 at 10:13pm
and 49 - 13 = 36
which one is the the bottem or the top
number in exponents
To understand where the numbers 49 and 36 came from in the given equation, let's break down the steps:
Starting with the equation x^2 - 14x + 13 = 30y, the goal is to isolate the term with x on one side of the equation.
1. Subtracting 30y from both sides: x^2 - 14x + 13 - 30y = 0.
2. Simplifying the equation: x^2 - 14x - 30y + 13 = 0.
3. Rearranging terms: x^2 - 14x - 30y = -13.
4. Now, to complete the square, we need to add a constant term to both sides of the equation to create a perfect trinomial square. The constant term is determined by taking half of the coefficient of the x term (which is -14), and squaring it. Half of -14 is -7, and squaring it gives us 49.
Adding 49 to both sides: x^2 - 14x - 30y + 13 + 49 = 49.
Simplifying further: x^2 - 14x - 30y + 62 = 49.
Rearranging terms: x^2 - 14x - 30y = 49 - 62.
Notice that on the left side of the equation, we have a perfect square trinomial: (x - 7)^2. On the right side, 49 - 62 equals -13. So, the equation becomes:
(x - 7)^2 = -13.
However, this equation doesn't provide a valid solution since a perfect square cannot be equal to a negative number. Therefore, there seems to be an error in the provided steps. The correct steps for this equation should be revisited to reach an accurate solution.