y^2=7y-7

Simple and best practice solution for y^2=7y-7 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 y^2=7y-7 equation:


Simplifying
y2 = 7y + -7

Reorder the terms:
y2 = -7 + 7y

Solving
y2 = -7 + 7y

Solving for variable 'y'.

Reorder the terms:
7 + -7y + y2 = -7 + 7y + 7 + -7y

Reorder the terms:
7 + -7y + y2 = -7 + 7 + 7y + -7y

Combine like terms: -7 + 7 = 0
7 + -7y + y2 = 0 + 7y + -7y
7 + -7y + y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
7 + -7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -7y + -7 + y2 = 0 + -7

Reorder the terms:
7 + -7 + -7y + y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -7y + y2 = 0 + -7
-7y + y2 = 0 + -7

Combine like terms: 0 + -7 = -7
-7y + y2 = -7

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -7 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -7 + 12.25

Combine like terms: -7 + 12.25 = 5.25
12.25 + -7y + y2 = 5.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(y + -3.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

y + -3.5 = 2.291287847 Simplifying y + -3.5 = 2.291287847 Reorder the terms: -3.5 + y = 2.291287847 Solving -3.5 + y = 2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 2.291287847 + 3.5 y = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 y = 5.791287847 Simplifying y = 5.791287847

Subproblem 2

y + -3.5 = -2.291287847 Simplifying y + -3.5 = -2.291287847 Reorder the terms: -3.5 + y = -2.291287847 Solving -3.5 + y = -2.291287847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -2.291287847 + 3.5 y = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 y = 1.208712153 Simplifying y = 1.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.791287847, 1.208712153}

See similar equations:

| 8x+17=6x+77 | | 47-4x=5x+15 | | (a-1)(a-4)x=a-2(x+1) | | 2a^2x+3=3a+2x | | 2x-15=22+92 | | (4x-6)(2x-1)= | | 9-7x=214-42x | | -47-3x=9x-10 | | 5x+x+3=x+15 | | 4x^2=160 | | 12a+(7a-5a)= | | 9x=81-49(x-3) | | 115-4x=14x+21 | | 9-9x=27-16x | | 133-3x=6x+7 | | 4x+3=2x+10 | | 2x^2-4xy+4y^2-6x+9=0 | | 3x+9=63x-3x | | 2(x-1)=3x-1 | | 5(x+11)=49 | | 2x+36=5x+12 | | -16t^2+48t=48 | | 5x-4-2x+5=15 | | 2x+5-5x-4=15 | | 16t^2+4t=420 | | 10x+14=22 | | 21*6=90 | | 3(3x-4)=5x+12 | | 3(3x+2)=5x+30 | | 2(3x-1)=3x-14 | | 4x+5=5(2x-1)-2 | | 5x+20=75 |

Equations solver categories