12w^2+32w+9=0

Simple and best practice solution for 12w^2+32w+9=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 12w^2+32w+9=0 equation: 


Simplifying
12w2 + 32w + 9 = 0

Reorder the terms:
9 + 32w + 12w2 = 0

Solving
9 + 32w + 12w2 = 0

Solving for variable 'w'.

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

Divide each side by '12'.
0.75 + 2.666666667w + w2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 2.666666667w + -0.75 + w2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 2.666666667w + w2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 2.666666667w + w2 = 0 + -0.75
2.666666667w + w2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
2.666666667w + w2 = -0.75

The w term is 2.666666667w.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667w + 1.777777780 + w2 = -0.75 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667w + w2 = -0.75 + 1.777777780

Combine like terms: -0.75 + 1.777777780 = 1.02777778
1.777777780 + 2.666666667w + w2 = 1.02777778

Factor a perfect square on the left side:
(w + 1.333333334)(w + 1.333333334) = 1.02777778

Calculate the square root of the right side: 1.013793756

Break this problem into two subproblems by setting 
(w + 1.333333334) equal to 1.013793756 and -1.013793756.


Subproblem 1
w + 1.333333334 = 1.013793756

Simplifying
w + 1.333333334 = 1.013793756

Reorder the terms:
1.333333334 + w = 1.013793756

Solving
1.333333334 + w = 1.013793756

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + w = 1.013793756 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + w = 1.013793756 + -1.333333334
w = 1.013793756 + -1.333333334

Combine like terms: 1.013793756 + -1.333333334 = -0.319539578
w = -0.319539578

Simplifying
w = -0.319539578


Subproblem 2
w + 1.333333334 = -1.013793756

Simplifying
w + 1.333333334 = -1.013793756

Reorder the terms:
1.333333334 + w = -1.013793756

Solving
1.333333334 + w = -1.013793756

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + w = -1.013793756 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + w = -1.013793756 + -1.333333334
w = -1.013793756 + -1.333333334

Combine like terms: -1.013793756 + -1.333333334 = -2.34712709
w = -2.34712709

Simplifying
w = -2.34712709


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.319539578, -2.34712709}

See similar equations:

| 12w^2+32w+9=0 | | 12w^2+32w+9=0 | | (x^2-7)+(4x+6)=90 | | 14+48=180 | | 6=-3+n | | 8k-(7+k)=-(7k+7) | | 73x=90 | | 9x+39=5x-11 | | 73x=80 | | 2d+7d=5+4d | | 75=90 | | 10y+2x=70 | | h=-81t^2+qt+c | | 2x-5+(-5)=13 | | 45(8x+3)=90 | | 30+4(18)= | | 8(t-6)+4t=4(3t+4)-10 | | -3x=-8x-15 | | 2x-5y+(-5)=13 | | 45+9x=90 | | 0.2(3.3h-4.6)-2.24h=22.8 | | 45+9x=180 | | 6x=-11-14x | | 0.1(x+60)+0.7x=22 | | logex=0 | | 35+11x=180 | | -7y+4z=10 | | 28+10x=3x | | -4(x-2)+2x=5x+8 | | -7y+4x=10 | | 3b-1=-16 | | -3=8n-5 |

Equations solver categories