31w+5w^2=31

Simple and best practice solution for 31w+5w^2=31 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 31w+5w^2=31 equation:


Simplifying
31w + 5w2 = 31

Solving
31w + 5w2 = 31

Solving for variable 'w'.

Reorder the terms:
-31 + 31w + 5w2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 31w + 5w2 = 0

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

Divide each side by '5'.
-6.2 + 6.2w + w2 = 0

Move the constant term to the right:

Add '6.2' to each side of the equation.
-6.2 + 6.2w + 6.2 + w2 = 0 + 6.2

Reorder the terms:
-6.2 + 6.2 + 6.2w + w2 = 0 + 6.2

Combine like terms: -6.2 + 6.2 = 0.0
0.0 + 6.2w + w2 = 0 + 6.2
6.2w + w2 = 0 + 6.2

Combine like terms: 0 + 6.2 = 6.2
6.2w + w2 = 6.2

The w term is 6.2w.  Take half its coefficient (3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
6.2w + 9.61 + w2 = 6.2 + 9.61

Reorder the terms:
9.61 + 6.2w + w2 = 6.2 + 9.61

Combine like terms: 6.2 + 9.61 = 15.81
9.61 + 6.2w + w2 = 15.81

Factor a perfect square on the left side:
(w + 3.1)(w + 3.1) = 15.81

Calculate the square root of the right side: 3.97617907

Break this problem into two subproblems by setting 
(w + 3.1) equal to 3.97617907 and -3.97617907.

Subproblem 1

w + 3.1 = 3.97617907 Simplifying w + 3.1 = 3.97617907 Reorder the terms: 3.1 + w = 3.97617907 Solving 3.1 + w = 3.97617907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + w = 3.97617907 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + w = 3.97617907 + -3.1 w = 3.97617907 + -3.1 Combine like terms: 3.97617907 + -3.1 = 0.87617907 w = 0.87617907 Simplifying w = 0.87617907

Subproblem 2

w + 3.1 = -3.97617907 Simplifying w + 3.1 = -3.97617907 Reorder the terms: 3.1 + w = -3.97617907 Solving 3.1 + w = -3.97617907 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + w = -3.97617907 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + w = -3.97617907 + -3.1 w = -3.97617907 + -3.1 Combine like terms: -3.97617907 + -3.1 = -7.07617907 w = -7.07617907 Simplifying w = -7.07617907

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.87617907, -7.07617907}

See similar equations:

| 2x+4y=126 | | 10a^2+11a-6=0 | | x^3-(5x^2)+6=0 | | (10-x)4=-40 | | 13x+9y-6x-8y+1= | | 3x-2ky+2=0 | | 5.6(0.5x-0.7)=15.68 | | 12ab+6+5ab+2= | | -3(x-10)=78 | | 600t=(800t+.75) | | 3y+7=8-5y | | 8(2+x)=-8 | | 9a-b-2a-10b=0 | | 14-1+5x=10-2x+5+4x | | 75=5r-10 | | 4(x+2)-5(x+2)=2 | | -5m+7=67 | | 1.2(2p-3)= | | 4+5n=49 | | -5+2=c-3 | | x+14=34 | | 10+6n=28 | | 9(6+v)=162 | | 5(x+10)+x=0 | | 18+31=-20k | | 12(0.5x-0.3)=18 | | 15n+6=3n+18 | | 11s-6+9+3s= | | 11y+16=18y+2 | | -9(8-x)-13=5 | | -18+31=-20k | | -2=-m-7 |

Equations solver categories