21y+14y^2=1000

Simple and best practice solution for 21y+14y^2=1000 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 21y+14y^2=1000 equation:


Simplifying
21y + 14y2 = 1000

Solving
21y + 14y2 = 1000

Solving for variable 'y'.

Reorder the terms:
-1000 + 21y + 14y2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 21y + 14y2 = 0

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

Divide each side by '14'.
-71.42857143 + 1.5y + y2 = 0

Move the constant term to the right:

Add '71.42857143' to each side of the equation.
-71.42857143 + 1.5y + 71.42857143 + y2 = 0 + 71.42857143

Reorder the terms:
-71.42857143 + 71.42857143 + 1.5y + y2 = 0 + 71.42857143

Combine like terms: -71.42857143 + 71.42857143 = 0.00000000
0.00000000 + 1.5y + y2 = 0 + 71.42857143
1.5y + y2 = 0 + 71.42857143

Combine like terms: 0 + 71.42857143 = 71.42857143
1.5y + y2 = 71.42857143

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = 71.42857143 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = 71.42857143 + 0.5625

Combine like terms: 71.42857143 + 0.5625 = 71.99107143
0.5625 + 1.5y + y2 = 71.99107143

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = 71.99107143

Calculate the square root of the right side: 8.484755237

Break this problem into two subproblems by setting 
(y + 0.75) equal to 8.484755237 and -8.484755237.

Subproblem 1

y + 0.75 = 8.484755237 Simplifying y + 0.75 = 8.484755237 Reorder the terms: 0.75 + y = 8.484755237 Solving 0.75 + y = 8.484755237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = 8.484755237 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = 8.484755237 + -0.75 y = 8.484755237 + -0.75 Combine like terms: 8.484755237 + -0.75 = 7.734755237 y = 7.734755237 Simplifying y = 7.734755237

Subproblem 2

y + 0.75 = -8.484755237 Simplifying y + 0.75 = -8.484755237 Reorder the terms: 0.75 + y = -8.484755237 Solving 0.75 + y = -8.484755237 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + y = -8.484755237 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + y = -8.484755237 + -0.75 y = -8.484755237 + -0.75 Combine like terms: -8.484755237 + -0.75 = -9.234755237 y = -9.234755237 Simplifying y = -9.234755237

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.734755237, -9.234755237}

See similar equations:

| -9+2x=x-4 | | 3p-5p=-p+5 | | 5x+10=500 | | x+3=12-13 | | 3=1000y-2y^2 | | -5-5n=100 | | 6lgx=0 | | 12x+8=128 | | 3/y=1000 | | 12x+8=120 | | tan(xy)=xy | | 3x+175.5=10x-53 | | 551=-19k | | 25x^3-36x= | | 7x+29=62+2x | | 15x=150-15x | | 3-5x+4=-1+3x | | 6r=114 | | 4/5x=-40 | | 8=8n-16 | | M-21=-28 | | 1-1/7x=-8= | | -16z=-14 | | 390=13n | | x^2*x+2x=135 | | x=3y^2+18y-20 | | 45x+7=60 | | -13+2x-5=-3 | | 102x=8 | | 12x+47y=5 | | 3(5x+8)=-33 | | 4x-7(-5x+16)=122 |

Equations solver categories