(y+7)y=5

Simple and best practice solution for (y+7)y=5 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+7)y=5 equation:


Simplifying
(y + 7) * y = 5

Reorder the terms:
(7 + y) * y = 5

Reorder the terms for easier multiplication:
y(7 + y) = 5
(7 * y + y * y) = 5
(7y + y2) = 5

Solving
7y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
-5 + 7y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 7y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 7y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 7y + y2 = 0 + 5
7y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
7y + y2 = 5

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 = 5 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 5 + 12.25

Combine like terms: 5 + 12.25 = 17.25
12.25 + 7y + y2 = 17.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(y + 3.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
y + 3.5 = 4.153311931

Simplifying
y + 3.5 = 4.153311931

Reorder the terms:
3.5 + y = 4.153311931

Solving
3.5 + y = 4.153311931

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 = 4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 4.153311931 + -3.5
y = 4.153311931 + -3.5

Combine like terms: 4.153311931 + -3.5 = 0.653311931
y = 0.653311931

Simplifying
y = 0.653311931


Subproblem 2
y + 3.5 = -4.153311931

Simplifying
y + 3.5 = -4.153311931

Reorder the terms:
3.5 + y = -4.153311931

Solving
3.5 + y = -4.153311931

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 = -4.153311931 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -4.153311931 + -3.5
y = -4.153311931 + -3.5

Combine like terms: -4.153311931 + -3.5 = -7.653311931
y = -7.653311931

Simplifying
y = -7.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.653311931, -7.653311931}

See similar equations:

| 14+3h=8h-3(h-4) | | 6m^2-2m=9 | | 2(u+1)+4u=3(2u-1)+8 | | 46+10n=6-2(1-8n) | | 5y-2.6=7.4 | | X^2-6xy-5y^2+4x-22=0 | | 12,600=s-12,600+12,600 | | 10(5g+2h-3)-4(3g-4h+2)= | | -3(5-9y)=25+7y | | 2x-5+5x=9 | | 0.375p-13=-25 | | 7x-2=23 | | y=10x-5 | | 15x-2=6x-7 | | 7(x-1)=3+2(2x+7) | | 98n^2-200= | | 9x(x-6)=0 | | -3x^2-x+2= | | -8(2a-3b)-5(6b-4a)= | | 4n^2+28n+40=280 | | -4x^2-4x+15= | | 3m-4n=-14 | | 5r^2-55r+120=0 | | x^2+-12x=-36 | | 3x^2-4x-5= | | .5x^2=0.2x+1 | | 12y^2+17y-5= | | 4n^2+28n+40=0 | | 3(4x-5)+4(2x+6)= | | 4x^2-31x+1= | | 4x+5y=-3 | | 3x^2-19x+20= |

Equations solver categories