2y(y+5)=7

Simple and best practice solution for 2y(y+5)=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 2y(y+5)=7 equation: 


Simplifying
2y(y + 5) = 7

Reorder the terms:
2y(5 + y) = 7
(5 * 2y + y * 2y) = 7
(10y + 2y2) = 7

Solving
10y + 2y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + 10y + 2y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 10y + 2y2 = 0

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

Divide each side by '2'.
-3.5 + 5y + y2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 5y + 3.5 + y2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 5y + y2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 5y + y2 = 0 + 3.5
5y + y2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
5y + y2 = 3.5

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 3.5 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 3.5 + 6.25

Combine like terms: 3.5 + 6.25 = 9.75
6.25 + 5y + y2 = 9.75

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
y + 2.5 = 3.122498999

Simplifying
y + 2.5 = 3.122498999

Reorder the terms:
2.5 + y = 3.122498999

Solving
2.5 + y = 3.122498999

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.122498999 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.122498999 + -2.5
y = 3.122498999 + -2.5

Combine like terms: 3.122498999 + -2.5 = 0.622498999
y = 0.622498999

Simplifying
y = 0.622498999


Subproblem 2
y + 2.5 = -3.122498999

Simplifying
y + 2.5 = -3.122498999

Reorder the terms:
2.5 + y = -3.122498999

Solving
2.5 + y = -3.122498999

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.122498999 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.122498999 + -2.5
y = -3.122498999 + -2.5

Combine like terms: -3.122498999 + -2.5 = -5.622498999
y = -5.622498999

Simplifying
y = -5.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.622498999, -5.622498999}

See similar equations:

| 5d=(-32) | | -20-k=-20 | | 3.8p+3=0.6p+31.8 | | 55x+6x+12x+5x+44x+18x= | | 13b=7 | | 16x=32x^2 | | 2x+2x+30=90 | | k-15=9-7k | | 19c=76 | | 4v+16=5(3-v)-8 | | 4q+97=-59 | | 5p+6p=11 | | 9w-16=-8+3w | | -2x-1/4(1+7x)=31/4-27x/4 | | 2x^2+x-5=0 | | 15XR=3000 | | -832=26y | | 14r-24=-94 | | -8+1=m-3 | | 39/5+18k/5=-4/5(-7k-1) | | x+(x+4)=221 | | -9x^2+30x+25=0 | | -7x^2+8+10x^2-12-5x= | | 3x+2y=1000 | | (2b+1)-b=4 | | n+(-3)=12 | | 4t=4 | | 16z^2+30z-54=0 | | 183d+3.5-20d=19.7 | | 5x+12-180= | | 30x+25=-9x | | c^2-21=43 |

Equations solver categories