xy=y^2-7x^2

Simple and best practice solution for xy=y^2-7x^2 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for xy=y^2-7x^2 equation:


Simplifying
xy = y2 + -7x2

Reorder the terms:
xy = -7x2 + y2

Solving
xy = -7x2 + y2

Solving for variable 'x'.

Reorder the terms:
xy + 7x2 + -1y2 = -7x2 + 7x2 + y2 + -1y2

Combine like terms: -7x2 + 7x2 = 0
xy + 7x2 + -1y2 = 0 + y2 + -1y2
xy + 7x2 + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
xy + 7x2 + -1y2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
0.1428571429xy + x2 + -0.1428571429y2 = 0

Move the constant term to the right:

Add '0.1428571429y2' to each side of the equation.
0.1428571429xy + x2 + -0.1428571429y2 + 0.1428571429y2 = 0 + 0.1428571429y2

Combine like terms: -0.1428571429y2 + 0.1428571429y2 = 0.0000000000
0.1428571429xy + x2 + 0.0000000000 = 0 + 0.1428571429y2
0.1428571429xy + x2 = 0 + 0.1428571429y2
Remove the zero:
0.1428571429xy + x2 = 0.1428571429y2

The x term is xy.  Take half its coefficient (0.5y).
Square it (0.25y2) and add it to both sides.

Add '0.25y2' to each side of the equation.
0.1428571429xy + x2 + 0.25y2 = 0.1428571429y2 + 0.25y2

Combine like terms: 0.1428571429y2 + 0.25y2 = 0.3928571429y2
0.1428571429xy + x2 + 0.25y2 = 0.3928571429y2

Factor a perfect square on the left side:
(x + 0.5y)(x + 0.5y) = 0.3928571429y2

Calculate the square root of the right side: 0.626783171y

Break this problem into two subproblems by setting 
(x + 0.5y) equal to 0.626783171y and -0.626783171y.


Subproblem 1
x + 0.5y = 0.626783171y

Simplifying
x + 0.5y = 0.626783171y

Solving
x + 0.5y = 0.626783171y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = 0.626783171y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = 0.626783171y + -0.5y
x = 0.626783171y + -0.5y

Combine like terms: 0.626783171y + -0.5y = 0.126783171y
x = 0.126783171y

Simplifying
x = 0.126783171y


Subproblem 2
x + 0.5y = -0.626783171y

Simplifying
x + 0.5y = -0.626783171y

Solving
x + 0.5y = -0.626783171y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5y' to each side of the equation.
x + 0.5y + -0.5y = -0.626783171y + -0.5y

Combine like terms: 0.5y + -0.5y = 0.0
x + 0.0 = -0.626783171y + -0.5y
x = -0.626783171y + -0.5y

Combine like terms: -0.626783171y + -0.5y = -1.126783171y
x = -1.126783171y

Simplifying
x = -1.126783171y


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.126783171y, -1.126783171y}

See similar equations:

| -5a+c+3y=2z | | x-6=-41 | | X^2-144+5x=0 | | -7a+6+8a=13-22 | | 6y+13y=180 | | 35+x+x+40+129=180 | | x^2+10+15=0 | | 7y-22+12-7=180 | | 4r+(5r+3)=23 | | x-(-38)=7 | | -4-5x=29 | | 13x-8+7x-8=180 | | (4w+7v)(5w-4v-3)=0 | | 5-15=2x+6 | | 175a^3b+343a^3b^3-63ab^3= | | 8a+a=5a | | -4(2y+1)-5=-4(y+6)+2y | | 6y+12=-6(y+8) | | 19x-17=91 | | graph-4y=-5x-18 | | 28=-7y+5(y+8) | | Ln(x)=-14 | | xln(x)-8+2ln(x)-4x=0 | | 14x+12=4x+292 | | -7x-8=-13-2x | | 46=4m-34 | | f(x)=-4.9x^2+10x+1200 | | x^2+17x-70=0 | | 49-7x=20x+19 | | 18x+6000=30x | | -14=-y+6 | | FV=PV(1+r)n |

Equations solver categories