3w^2+7w-16=0

Simple and best practice solution for 3w^2+7w-16=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 3w^2+7w-16=0 equation: 


Simplifying
3w2 + 7w + -16 = 0

Reorder the terms:
-16 + 7w + 3w2 = 0

Solving
-16 + 7w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-5.333333333 + 2.333333333w + w2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 2.333333333w + 5.333333333 + w2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 2.333333333w + w2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 2.333333333w + w2 = 0 + 5.333333333
2.333333333w + w2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
2.333333333w + w2 = 5.333333333

The w term is 2.333333333w.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333w + 1.361111112 + w2 = 5.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333w + w2 = 5.333333333 + 1.361111112

Combine like terms: 5.333333333 + 1.361111112 = 6.694444445
1.361111112 + 2.333333333w + w2 = 6.694444445

Factor a perfect square on the left side:
(w + 1.166666667)(w + 1.166666667) = 6.694444445

Calculate the square root of the right side: 2.587362449

Break this problem into two subproblems by setting 
(w + 1.166666667) equal to 2.587362449 and -2.587362449.


Subproblem 1
w + 1.166666667 = 2.587362449

Simplifying
w + 1.166666667 = 2.587362449

Reorder the terms:
1.166666667 + w = 2.587362449

Solving
1.166666667 + w = 2.587362449

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = 2.587362449 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = 2.587362449 + -1.166666667
w = 2.587362449 + -1.166666667

Combine like terms: 2.587362449 + -1.166666667 = 1.420695782
w = 1.420695782

Simplifying
w = 1.420695782


Subproblem 2
w + 1.166666667 = -2.587362449

Simplifying
w + 1.166666667 = -2.587362449

Reorder the terms:
1.166666667 + w = -2.587362449

Solving
1.166666667 + w = -2.587362449

Solving for variable 'w'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + w = -2.587362449 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + w = -2.587362449 + -1.166666667
w = -2.587362449 + -1.166666667

Combine like terms: -2.587362449 + -1.166666667 = -3.754029116
w = -3.754029116

Simplifying
w = -3.754029116


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.420695782, -3.754029116}

See similar equations:

| 4[9-(7x-3)]=140x+96 | | 1.1x=5 | | -7/16×-16-26 | | -4w+12=-8(w+2) | | 8y^4+56y^3= | | (28-2X)+(20-2X)=240 | | 2x^2+6=9x | | 200+10m=400 | | 7+5x+4x=8 | | 175n^2-448=0 | | 4x/20 | | f(n+1)=f(n)-5 | | 12.75x=1.5x | | 5w^3+5w^2-130w+120=0 | | -7/16×-16-26=-19 | | 1/2=1/6d | | 12-1/2r=2-1/2 | | -5+3x+3x=1 | | -7/16(-16-26)=-19 | | 20x+15=500-10x | | 8cos(x)-4=0 | | z=3+(5x-14)i | | 2500+150m=10000 | | 10m(m+3)=13m-3 | | 17x=2x | | 2b+5a-6b-a= | | -27a+70-40a-8= | | 12-2w=42 | | 50-5d=15 | | 2(x-3)-1=7x | | 5u-12=53 | | -(4x-8y)= |

Equations solver categories