31y^2+8y-7=0

Simple and best practice solution for 31y^2+8y-7=0 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 31y^2+8y-7=0 equation:


Simplifying
31y2 + 8y + -7 = 0

Reorder the terms:
-7 + 8y + 31y2 = 0

Solving
-7 + 8y + 31y2 = 0

Solving for variable 'y'.

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

Divide each side by '31'.
-0.2258064516 + 0.2580645161y + y2 = 0

Move the constant term to the right:

Add '0.2258064516' to each side of the equation.
-0.2258064516 + 0.2580645161y + 0.2258064516 + y2 = 0 + 0.2258064516

Reorder the terms:
-0.2258064516 + 0.2258064516 + 0.2580645161y + y2 = 0 + 0.2258064516

Combine like terms: -0.2258064516 + 0.2258064516 = 0.0000000000
0.0000000000 + 0.2580645161y + y2 = 0 + 0.2258064516
0.2580645161y + y2 = 0 + 0.2258064516

Combine like terms: 0 + 0.2258064516 = 0.2258064516
0.2580645161y + y2 = 0.2258064516

The y term is 0.2580645161y.  Take half its coefficient (0.1290322581).
Square it (0.01664932363) and add it to both sides.

Add '0.01664932363' to each side of the equation.
0.2580645161y + 0.01664932363 + y2 = 0.2258064516 + 0.01664932363

Reorder the terms:
0.01664932363 + 0.2580645161y + y2 = 0.2258064516 + 0.01664932363

Combine like terms: 0.2258064516 + 0.01664932363 = 0.24245577523
0.01664932363 + 0.2580645161y + y2 = 0.24245577523

Factor a perfect square on the left side:
(y + 0.1290322581)(y + 0.1290322581) = 0.24245577523

Calculate the square root of the right side: 0.492397985

Break this problem into two subproblems by setting 
(y + 0.1290322581) equal to 0.492397985 and -0.492397985.

Subproblem 1

y + 0.1290322581 = 0.492397985 Simplifying y + 0.1290322581 = 0.492397985 Reorder the terms: 0.1290322581 + y = 0.492397985 Solving 0.1290322581 + y = 0.492397985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + y = 0.492397985 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + y = 0.492397985 + -0.1290322581 y = 0.492397985 + -0.1290322581 Combine like terms: 0.492397985 + -0.1290322581 = 0.3633657269 y = 0.3633657269 Simplifying y = 0.3633657269

Subproblem 2

y + 0.1290322581 = -0.492397985 Simplifying y + 0.1290322581 = -0.492397985 Reorder the terms: 0.1290322581 + y = -0.492397985 Solving 0.1290322581 + y = -0.492397985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1290322581' to each side of the equation. 0.1290322581 + -0.1290322581 + y = -0.492397985 + -0.1290322581 Combine like terms: 0.1290322581 + -0.1290322581 = 0.0000000000 0.0000000000 + y = -0.492397985 + -0.1290322581 y = -0.492397985 + -0.1290322581 Combine like terms: -0.492397985 + -0.1290322581 = -0.6214302431 y = -0.6214302431 Simplifying y = -0.6214302431

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.3633657269, -0.6214302431}

See similar equations:

| 3b+6=9b | | 3b+6= | | 6y^2+19y+15=0 | | 2a+4= | | 6y^2+19m+15=0 | | 3x+5x=230 | | 2[4-5(3x-5)]=60-15x | | y=x^2+5x-22 | | 3(2*x)+4x=110-14 | | ln(x+6)=0 | | -14-28=10x-3x | | 2(x*2)=68 | | 2(2*2)=68 | | 4(5x)=60 | | -5y=-40 | | 2x=-26 | | 3x=42 | | -2+4+x=-3+17 | | lnx-5lnx=10lnx | | 14x+2y=74 | | y=3x+11 | | ln(x+6)=2lnx | | 5-11=a+2-13 | | 30x+27=-45x-6 | | 3f-4=24 | | 12x-6=5x+22 | | 8x-32-7x=6 | | 14x+15=7x+49 | | 2(x-4)=-4x+22 | | 8x-5=2x+13 | | 47-4x=14x+17 | | 16x+15=8x+31 |

Equations solver categories