31.5=2w^2-4w

Simple and best practice solution for 31.5=2w^2-4w 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 31.5=2w^2-4w equation:


Simplifying
31.5 = 2w2 + -4w

Reorder the terms:
31.5 = -4w + 2w2

Solving
31.5 = -4w + 2w2

Solving for variable 'w'.

Reorder the terms:
31.5 + 4w + -2w2 = -4w + 4w + 2w2 + -2w2

Combine like terms: -4w + 4w = 0
31.5 + 4w + -2w2 = 0 + 2w2 + -2w2
31.5 + 4w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
31.5 + 4w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-15.75 + -2w + w2 = 0

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + -2w + 15.75 + w2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + -2w + w2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + -2w + w2 = 0 + 15.75
-2w + w2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
-2w + w2 = 15.75

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 15.75 + 1

Reorder the terms:
1 + -2w + w2 = 15.75 + 1

Combine like terms: 15.75 + 1 = 16.75
1 + -2w + w2 = 16.75

Factor a perfect square on the left side:
(w + -1)(w + -1) = 16.75

Calculate the square root of the right side: 4.092676386

Break this problem into two subproblems by setting 
(w + -1) equal to 4.092676386 and -4.092676386.

Subproblem 1

w + -1 = 4.092676386 Simplifying w + -1 = 4.092676386 Reorder the terms: -1 + w = 4.092676386 Solving -1 + w = 4.092676386 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 4.092676386 + 1 Combine like terms: -1 + 1 = 0 0 + w = 4.092676386 + 1 w = 4.092676386 + 1 Combine like terms: 4.092676386 + 1 = 5.092676386 w = 5.092676386 Simplifying w = 5.092676386

Subproblem 2

w + -1 = -4.092676386 Simplifying w + -1 = -4.092676386 Reorder the terms: -1 + w = -4.092676386 Solving -1 + w = -4.092676386 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -4.092676386 + 1 Combine like terms: -1 + 1 = 0 0 + w = -4.092676386 + 1 w = -4.092676386 + 1 Combine like terms: -4.092676386 + 1 = -3.092676386 w = -3.092676386 Simplifying w = -3.092676386

Solution

The solution to the problem is based on the solutions from the subproblems. w = {5.092676386, -3.092676386}

See similar equations:

| 7j+6= | | 301.44=3.14*r^2*18 | | 8p-10=150 | | S-6=42 | | -38=2b+25(-7b) | | 3x*9=81 | | 3b+3= | | 2m-(m+5)=6+(m+1) | | 5-6x=ln*3.25 | | 3/4x-3/2=10/3x-1 | | 4(y-1)=3y+5 | | P+14=59 | | 4y-5+53=8y+50-5y | | ax(a+6)=40 | | 8x-2x+4=20 | | 63=3+9 | | 2x+5x-1=90 | | Log(X-15)-2=-Log(X) | | 9/y=18 | | 25Cos^2-4=0 | | -6(1-5d)=30 | | 5X-50=150 | | 17/7 | | 2x^2-4x+10=x^2+5x-8 | | 2(x+6)=4(x+5) | | 3y/4=36 | | -3x+17=-4x-24 | | 6-9u-2u^2+3u^3=0 | | -104=8x+16 | | 1/3x=7/15 | | -3+17=-4x-24 | | y^2-2y+2=3y-2 |

Equations solver categories