3w^2+7w=120

Simple and best practice solution for 3w^2+7w=120 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=120 equation:


Simplifying
3w2 + 7w = 120

Reorder the terms:
7w + 3w2 = 120

Solving
7w + 3w2 = 120

Solving for variable 'w'.

Reorder the terms:
-120 + 7w + 3w2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 7w + 3w2 = 0

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

Divide each side by '3'.
-40 + 2.333333333w + w2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + 2.333333333w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + 2.333333333w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + 2.333333333w + w2 = 0 + 40
2.333333333w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
2.333333333w + w2 = 40

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 = 40 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333w + w2 = 40 + 1.361111112

Combine like terms: 40 + 1.361111112 = 41.361111112
1.361111112 + 2.333333333w + w2 = 41.361111112

Factor a perfect square on the left side:
(w + 1.166666667)(w + 1.166666667) = 41.361111112

Calculate the square root of the right side: 6.431260461

Break this problem into two subproblems by setting 
(w + 1.166666667) equal to 6.431260461 and -6.431260461.

Subproblem 1

w + 1.166666667 = 6.431260461 Simplifying w + 1.166666667 = 6.431260461 Reorder the terms: 1.166666667 + w = 6.431260461 Solving 1.166666667 + w = 6.431260461 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 = 6.431260461 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + w = 6.431260461 + -1.166666667 w = 6.431260461 + -1.166666667 Combine like terms: 6.431260461 + -1.166666667 = 5.264593794 w = 5.264593794 Simplifying w = 5.264593794

Subproblem 2

w + 1.166666667 = -6.431260461 Simplifying w + 1.166666667 = -6.431260461 Reorder the terms: 1.166666667 + w = -6.431260461 Solving 1.166666667 + w = -6.431260461 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 = -6.431260461 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + w = -6.431260461 + -1.166666667 w = -6.431260461 + -1.166666667 Combine like terms: -6.431260461 + -1.166666667 = -7.597927128 w = -7.597927128 Simplifying w = -7.597927128

Solution

The solution to the problem is based on the solutions from the subproblems. w = {5.264593794, -7.597927128}

See similar equations:

| 3(x+2)=4x+6-2x+2 | | 5x+6+7=93 | | 2x+1/6=-11/6 | | 2(4y-3)=6y | | 5x+4x-2x=40+9 | | 4-16=z/-9 | | 4x^2+26x-47=0 | | 10x-12x=-16+60 | | 4a-(x+7)=13-5 | | 4y-5/3=7/3 | | 11w-17w=24 | | 1/7x-3=-9 | | 2(4x+5)=13x+6-5x+4 | | 4x+8(51)=40 | | 5n^2-3=42 | | -4x+9+8x=49 | | 2x+9x=3 | | 10x^2-300x+1250=0 | | 12x+10=58 | | 6x+4x+5=55 | | x/3-x/7=8 | | 10x^2-300x-1250=0 | | 3(x/4)=-12x | | 0.04P+0.06(1700-P)=75 | | 2x+16/x+24 | | -6x+4=10 | | x+2(51)=10 | | -5-8x^2=133 | | -0.7(0.06+5x)=-3.4x | | -9+3x+9y-10= | | 4x-7(51)=11 | | 4x+7+(4x+7-4)+(4x+7*2)=180 |

Equations solver categories