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 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

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