0=w^2+3w-196

Simple and best practice solution for 0=w^2+3w-196 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 0=w^2+3w-196 equation:


Simplifying
0 = w2 + 3w + -196

Reorder the terms:
0 = -196 + 3w + w2

Solving
0 = -196 + 3w + w2

Solving for variable 'w'.

Combine like terms: 0 + 196 = 196
196 + -3w + -1w2 = -196 + 3w + w2 + 196 + -3w + -1w2

Reorder the terms:
196 + -3w + -1w2 = -196 + 196 + 3w + -3w + w2 + -1w2

Combine like terms: -196 + 196 = 0
196 + -3w + -1w2 = 0 + 3w + -3w + w2 + -1w2
196 + -3w + -1w2 = 3w + -3w + w2 + -1w2

Combine like terms: 3w + -3w = 0
196 + -3w + -1w2 = 0 + w2 + -1w2
196 + -3w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
196 + -3w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-196 + 3w + w2 = 0

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + 3w + 196 + w2 = 0 + 196

Reorder the terms:
-196 + 196 + 3w + w2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + 3w + w2 = 0 + 196
3w + w2 = 0 + 196

Combine like terms: 0 + 196 = 196
3w + w2 = 196

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 196 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 196 + 2.25

Combine like terms: 196 + 2.25 = 198.25
2.25 + 3w + w2 = 198.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 198.25

Calculate the square root of the right side: 14.08012784

Break this problem into two subproblems by setting 
(w + 1.5) equal to 14.08012784 and -14.08012784.

Subproblem 1

w + 1.5 = 14.08012784 Simplifying w + 1.5 = 14.08012784 Reorder the terms: 1.5 + w = 14.08012784 Solving 1.5 + w = 14.08012784 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 14.08012784 + -1.5 w = 14.08012784 + -1.5 Combine like terms: 14.08012784 + -1.5 = 12.58012784 w = 12.58012784 Simplifying w = 12.58012784

Subproblem 2

w + 1.5 = -14.08012784 Simplifying w + 1.5 = -14.08012784 Reorder the terms: 1.5 + w = -14.08012784 Solving 1.5 + w = -14.08012784 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -14.08012784 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -14.08012784 + -1.5 w = -14.08012784 + -1.5 Combine like terms: -14.08012784 + -1.5 = -15.58012784 w = -15.58012784 Simplifying w = -15.58012784

Solution

The solution to the problem is based on the solutions from the subproblems. w = {12.58012784, -15.58012784}

See similar equations:

| 11x+2+x=50 | | 585.00+0.13x=786.1905 | | x-0.25x=9 | | 3/2a-8=19 | | 7(1-7k)-7=3k | | 7x+4/6=x+3 | | X-4=15*5 | | 21r+7(r+1/7(1+7R)) | | (x+1)=3x+4 | | 4+c=-1/4 | | 3/4d+1/2=7/8 | | 5(lnx)-8=0 | | -2+n/9=-1 | | 8x-15-3x=15 | | 12/5h-2h | | (-104/21)=b-5(11/14) | | 6(2-4x)=180 | | 0.4(2r+3)=0.6+3.6 | | F/2-F-8/4=9/4 | | 25n=5n+20 | | 9/10+(-26/35) | | -2/7x+3x=5/7x+1/2 | | 2x-7x-11=-5x+5-11 | | -2=-2+7x | | 1/3(3.14)16h=12(3.14) | | 4x+3+5x-10=7x+15 | | 6x-3x+5=68 | | 6(p-2)-3(4-2p)=2p+1 | | a/-3=9x | | 3d-5=7d-21 | | -4=b/9-3 | | k+10/2=-7 |

Equations solver categories