# Find the Quadratic Constant of Variation 49x^2=81y^2+3969

49×2=81y2+3969
Rewrite the equation as 81y2+3969=49×2.
81y2+3969=49×2
Subtract 3969 from both sides of the equation.
81y2=49×2-3969
Divide each term by 81 and simplify.
Divide each term in 81y2=49×2-3969 by 81.
81y281=49×281+-396981
Cancel the common factor of 81.
Cancel the common factor.
81y281=49×281+-396981
Divide y2 by 1.
y2=49×281+-396981
y2=49×281+-396981
Divide -3969 by 81.
y2=49×281-49
y2=49×281-49
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±49×281-49
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Factor 49 out of 49×281-49.
Factor 49 out of 49×281.
y=±49(x281)-49
Factor 49 out of -49.
y=±49(x281)+49(-1)
Factor 49 out of 49×281+49(-1).
y=±49(x281-1)
y=±49(x281-1)
Rewrite 81 as 92.
y=±49(x292-1)
Rewrite x292 as (x9)2.
y=±49((x9)2-1)
Rewrite 1 as 12.
y=±49((x9)2-12)
Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x9 and b=1.
y=±49(x9+1)(x9-1)
Write 1 as a fraction with a common denominator.
y=±49(x9+99)(x9-1)
Combine the numerators over the common denominator.
y=±49(x+99)⋅(x9-1)
To write -1 as a fraction with a common denominator, multiply by 99.
y=±49(x+99)⋅(x9-1⋅99)
Combine -1 and 99.
y=±49(x+99)⋅(x9+-1⋅99)
Combine the numerators over the common denominator.
y=±49(x+99)⋅x-1⋅99
Multiply -1 by 9.
y=±49(x+99)⋅x-99
Combine 49 and x+99.
y=±49(x+9)9⋅x-99
Multiply 49(x+9)9 and x-99.
y=±49(x+9)(x-9)9⋅9
Multiply 9 by 9.
y=±49(x+9)(x-9)81
Rewrite 49(x+9)(x-9)81 as (79)2((x+32)(x-9)).
Factor the perfect power 72 out of 49(x+9)(x-9).
y=±72((x+32)(x-9))81
Factor the perfect power 92 out of 81.
y=±72((x+32)(x-9))92⋅1
Rearrange the fraction 72((x+32)(x-9))92⋅1.
y=±(79)2((x+32)(x-9))
y=±(79)2((x+32)(x-9))
Pull terms out from under the radical.
y=±79⋅(x+32)(x-9)
Raise 3 to the power of 2.
y=±79⋅(x+9)(x-9)
Combine 79 and (x+9)(x-9).
y=±7(x+9)(x-9)9
y=±7(x+9)(x-9)9
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=7(x+9)(x-9)9
Next, use the negative value of the ± to find the second solution.
y=-7(x+9)(x-9)9
The complete solution is the result of both the positive and negative portions of the solution.
y=7(x+9)(x-9)9
y=-7(x+9)(x-9)9
y=7(x+9)(x-9)9
y=-7(x+9)(x-9)9
y=7(x+9)(x-9)9
y=-7(x+9)(x-9)9
The given equation y=7(x+9)(x-9)9,-7(x+9)(x-9)9 can not be written as y=kx2, so y doesn’t vary directly with x2.
y doesn’t vary directly with x
Find the Quadratic Constant of Variation 49x^2=81y^2+3969