20y^2+10y=148

Simple and best practice solution for 20y^2+10y=148 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 20y^2+10y=148 equation: 


Simplifying
20y2 + 10y = 148

Reorder the terms:
10y + 20y2 = 148

Solving
10y + 20y2 = 148

Solving for variable 'y'.

Reorder the terms:
-148 + 10y + 20y2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + 10y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-74 + 5y + 10y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-74 + 5y + 10y2)' equal to zero and attempt to solve:

Simplifying
-74 + 5y + 10y2 = 0

Solving
-74 + 5y + 10y2 = 0

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

Divide each side by '10'.
-7.4 + 0.5y + y2 = 0.0

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + 0.5y + 7.4 + y2 = 0.0 + 7.4

Reorder the terms:
-7.4 + 7.4 + 0.5y + y2 = 0.0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + 0.5y + y2 = 0.0 + 7.4
0.5y + y2 = 0.0 + 7.4

Combine like terms: 0.0 + 7.4 = 7.4
0.5y + y2 = 7.4

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = 7.4 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = 7.4 + 0.0625

Combine like terms: 7.4 + 0.0625 = 7.4625
0.0625 + 0.5y + y2 = 7.4625

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 7.4625

Calculate the square root of the right side: 2.731757676

Break this problem into two subproblems by setting 
(y + 0.25) equal to 2.731757676 and -2.731757676.


Subproblem 1
y + 0.25 = 2.731757676

Simplifying
y + 0.25 = 2.731757676

Reorder the terms:
0.25 + y = 2.731757676

Solving
0.25 + y = 2.731757676

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 2.731757676 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 2.731757676 + -0.25
y = 2.731757676 + -0.25

Combine like terms: 2.731757676 + -0.25 = 2.481757676
y = 2.481757676

Simplifying
y = 2.481757676


Subproblem 2
y + 0.25 = -2.731757676

Simplifying
y + 0.25 = -2.731757676

Reorder the terms:
0.25 + y = -2.731757676

Solving
0.25 + y = -2.731757676

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = -2.731757676 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = -2.731757676 + -0.25
y = -2.731757676 + -0.25

Combine like terms: -2.731757676 + -0.25 = -2.981757676
y = -2.981757676

Simplifying
y = -2.981757676


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.481757676, -2.981757676}
Solution
y = {2.481757676, -2.981757676}

See similar equations:

| -1/2y-8/3=-9/-5 | | h(t)=-12t^2+34t+28 | | 2(4x-7)=5(x+3) | | 8-8(4-7x)=0 | | (9x-1)+(6x+58)=90 | | 1/2(13x-3( | | (9x-12)*16=754 | | z^4+2+4i=0 | | -1/2y-8/3=-9/5 | | 12=5y+4 | | 3-7(x+4)+8=-4x-10-2x | | -4y-19=-3 | | 16=m-15 | | 5m+-14=-49 | | (7x-9)+(4x+22)=180 | | s^2-8s+3=0 | | n-(1.5)=1.5 | | -2x+4=7(x+7) | | 55-n=34.25 | | 2w+4x+18=14x+4 | | 4+4n=3n | | -4(2x-1)=-6+13+x | | -7y+8=21x-6 | | (5/4)=(x-3/x-4) | | log(4)(2x)-6=2 | | z^2+2z=33 | | 7bn+12=-23 | | -3x-25=-5x+9 | | 3/6x=15 | | 4x+2(2x+3)=14 | | 1-6w=-59 | | (4x+52)+(8x-10)=180 |

Equations solver categories