y(2y+4)=77

Simple and best practice solution for y(2y+4)=77 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(2y+4)=77 equation:


Simplifying
y(2y + 4) = 77

Reorder the terms:
y(4 + 2y) = 77
(4 * y + 2y * y) = 77
(4y + 2y2) = 77

Solving
4y + 2y2 = 77

Solving for variable 'y'.

Reorder the terms:
-77 + 4y + 2y2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 4y + 2y2 = 0

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

Divide each side by '2'.
-38.5 + 2y + y2 = 0

Move the constant term to the right:

Add '38.5' to each side of the equation.
-38.5 + 2y + 38.5 + y2 = 0 + 38.5

Reorder the terms:
-38.5 + 38.5 + 2y + y2 = 0 + 38.5

Combine like terms: -38.5 + 38.5 = 0.0
0.0 + 2y + y2 = 0 + 38.5
2y + y2 = 0 + 38.5

Combine like terms: 0 + 38.5 = 38.5
2y + y2 = 38.5

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 38.5 + 1

Reorder the terms:
1 + 2y + y2 = 38.5 + 1

Combine like terms: 38.5 + 1 = 39.5
1 + 2y + y2 = 39.5

Factor a perfect square on the left side:
(y + 1)(y + 1) = 39.5

Calculate the square root of the right side: 6.284902545

Break this problem into two subproblems by setting 
(y + 1) equal to 6.284902545 and -6.284902545.

Subproblem 1

y + 1 = 6.284902545 Simplifying y + 1 = 6.284902545 Reorder the terms: 1 + y = 6.284902545 Solving 1 + y = 6.284902545 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 6.284902545 + -1 Combine like terms: 1 + -1 = 0 0 + y = 6.284902545 + -1 y = 6.284902545 + -1 Combine like terms: 6.284902545 + -1 = 5.284902545 y = 5.284902545 Simplifying y = 5.284902545

Subproblem 2

y + 1 = -6.284902545 Simplifying y + 1 = -6.284902545 Reorder the terms: 1 + y = -6.284902545 Solving 1 + y = -6.284902545 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -6.284902545 + -1 Combine like terms: 1 + -1 = 0 0 + y = -6.284902545 + -1 y = -6.284902545 + -1 Combine like terms: -6.284902545 + -1 = -7.284902545 y = -7.284902545 Simplifying y = -7.284902545

Solution

The solution to the problem is based on the solutions from the subproblems. y = {5.284902545, -7.284902545}

See similar equations:

| x+15=65 | | -10-4p=22 | | 3x+5=6x-28 | | a-8=17 | | 45p+10q= | | 5(1+2p)=7p-1 | | -15-3p=6 | | 7+4b=4(1+b)+3 | | r+16=44 | | -5g+(8-g)=12 | | -47-7m=2 | | 3x^2-7x+12.25=13.25 | | m+1+5=0 | | -5x^2+7x+2=0 | | -42-6m=-12 | | 21g-12=98 | | 28x+4= | | 8n+2n=10+5n+7n | | 6(1-5n)=-8n-38 | | 4x(x-8)+10=-10 | | 4x(x-8)+10=-10 | | 17-8n=-4n+7(1-2n) | | -34-4m=-18 | | 4(x+5)-4=20-4x-4+8x | | 12-2=15-7x | | 6x+4-x=2(x+1) | | -29-3m=-20 | | 2n+-4=2 | | 14x=388+6y | | -16+g=-52 | | m-18=-264 | | 4n-4=4n-5 |

Equations solver categories