3y^2-2y+5=10y+1

Simple and best practice solution for 3y^2-2y+5=10y+1 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 3y^2-2y+5=10y+1 equation:


Simplifying
3y2 + -2y + 5 = 10y + 1

Reorder the terms:
5 + -2y + 3y2 = 10y + 1

Reorder the terms:
5 + -2y + 3y2 = 1 + 10y

Solving
5 + -2y + 3y2 = 1 + 10y

Solving for variable 'y'.

Reorder the terms:
5 + -1 + -2y + -10y + 3y2 = 1 + 10y + -1 + -10y

Combine like terms: 5 + -1 = 4
4 + -2y + -10y + 3y2 = 1 + 10y + -1 + -10y

Combine like terms: -2y + -10y = -12y
4 + -12y + 3y2 = 1 + 10y + -1 + -10y

Reorder the terms:
4 + -12y + 3y2 = 1 + -1 + 10y + -10y

Combine like terms: 1 + -1 = 0
4 + -12y + 3y2 = 0 + 10y + -10y
4 + -12y + 3y2 = 10y + -10y

Combine like terms: 10y + -10y = 0
4 + -12y + 3y2 = 0

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

Divide each side by '3'.
1.333333333 + -4y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -4y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -4y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -4y + y2 = 0 + -1.333333333
-4y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-4y + y2 = -1.333333333

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -1.333333333 + 4

Reorder the terms:
4 + -4y + y2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + -4y + y2 = 2.666666667

Factor a perfect square on the left side:
(y + -2)(y + -2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(y + -2) equal to 1.632993162 and -1.632993162.

Subproblem 1

y + -2 = 1.632993162 Simplifying y + -2 = 1.632993162 Reorder the terms: -2 + y = 1.632993162 Solving -2 + y = 1.632993162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.632993162 + 2 y = 1.632993162 + 2 Combine like terms: 1.632993162 + 2 = 3.632993162 y = 3.632993162 Simplifying y = 3.632993162

Subproblem 2

y + -2 = -1.632993162 Simplifying y + -2 = -1.632993162 Reorder the terms: -2 + y = -1.632993162 Solving -2 + y = -1.632993162 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.632993162 + 2 y = -1.632993162 + 2 Combine like terms: -1.632993162 + 2 = 0.367006838 y = 0.367006838 Simplifying y = 0.367006838

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.632993162, 0.367006838}

See similar equations:

| 33=11m^2 | | 24y-13-10y=-10+(25y-9)+(6y-10) | | -11-18y=19-(-15y-8) | | -(-22x-27)+24x=-7+(6x-22) | | 9n+9=99 | | 10z+(-7z-13)=10+29z-11 | | 6p^2+24p+24=0 | | (n-5)*4=8 | | 6x=26+(17x+25)+(-26x+6) | | 1+1/x=12/x^2 | | 2x(x-10)=4(x-8) | | 0.2=--/--- | | 7+(-30z-29)+(11z+8)-25z=17 | | 13z+21z+24z=8+6z | | 30y+25y=-9y+5-20y+25 | | 11x+2=24 | | 3/4z=-7/z-1/7+6 | | 7208/-220 | | 11y-6/3=7y+4/4-4/3 | | 5(3x+12)=13 | | -3z-7/5+9z/7=4z-7/9 | | 3y-8/2=-4y+2/5-8y/7 | | 2-6z-3=17z-7/7 | | 19-7a=(a+6)-8(5+2a) | | 4/3+8y/5-4y/3=8y/5+3/5 | | -2+8x/7=-3x+8x/5+1/2 | | 7208-220x=7920 | | -4/5-5x/2=7/4 | | 7x/2+2/3=7/4 | | 9-5z/2=0 | | 3x+5x+7=9x+4 | | 1/3-3y/4=0 |

Equations solver categories