3=w(w-6)-7w

Simple and best practice solution for 3=w(w-6)-7w 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 3=w(w-6)-7w equation:


Simplifying
3 = w(w + -6) + -7w

Reorder the terms:
3 = w(-6 + w) + -7w
3 = (-6 * w + w * w) + -7w
3 = (-6w + w2) + -7w

Reorder the terms:
3 = -6w + -7w + w2

Combine like terms: -6w + -7w = -13w
3 = -13w + w2

Solving
3 = -13w + w2

Solving for variable 'w'.

Reorder the terms:
3 + 13w + -1w2 = -13w + 13w + w2 + -1w2

Combine like terms: -13w + 13w = 0
3 + 13w + -1w2 = 0 + w2 + -1w2
3 + 13w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
3 + 13w + -1w2 = 0

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

Divide each side by '-1'.
-3 + -13w + w2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -13w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + -13w + w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -13w + w2 = 0 + 3
-13w + w2 = 0 + 3

Combine like terms: 0 + 3 = 3
-13w + w2 = 3

The w term is -13w.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13w + 42.25 + w2 = 3 + 42.25

Reorder the terms:
42.25 + -13w + w2 = 3 + 42.25

Combine like terms: 3 + 42.25 = 45.25
42.25 + -13w + w2 = 45.25

Factor a perfect square on the left side:
(w + -6.5)(w + -6.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(w + -6.5) equal to 6.726812024 and -6.726812024.

Subproblem 1

w + -6.5 = 6.726812024 Simplifying w + -6.5 = 6.726812024 Reorder the terms: -6.5 + w = 6.726812024 Solving -6.5 + w = 6.726812024 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = 6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = 6.726812024 + 6.5 w = 6.726812024 + 6.5 Combine like terms: 6.726812024 + 6.5 = 13.226812024 w = 13.226812024 Simplifying w = 13.226812024

Subproblem 2

w + -6.5 = -6.726812024 Simplifying w + -6.5 = -6.726812024 Reorder the terms: -6.5 + w = -6.726812024 Solving -6.5 + w = -6.726812024 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + w = -6.726812024 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + w = -6.726812024 + 6.5 w = -6.726812024 + 6.5 Combine like terms: -6.726812024 + 6.5 = -0.226812024 w = -0.226812024 Simplifying w = -0.226812024

Solution

The solution to the problem is based on the solutions from the subproblems. w = {13.226812024, -0.226812024}

See similar equations:

| 3p+(7)(1-p)= | | 45x+y=-50 | | 7a+3a=4a+100 | | 8z+2z=50 | | (1-2p)x^2+8px-(2+8p)=0 | | 125=5(12-x) | | 3.6(x+2.6)=54 | | 4p=20+30 | | y^2-2y-4x-3=0 | | 12x*x-6x=0 | | 1.5(z+2)=90 | | 13(x-8)=-91 | | 8p+(-5)(1-p)= | | Px^2+(2p+2)x+p+7=0 | | 3.2x-9=39 | | 6x^3+12x^2+4x=8 | | 0.107=0.1799*X+0.530*10 | | 2.2x-4.4=20 | | 8x^7-56x^6+96x^5=0 | | 3b+4b=16-b | | 2x-4=26-x | | (3x+4)x(2x+5)= | | 30+2V=15+74 | | 300x^2+20000x+58000000=0 | | 3x-4(2x)=3x+17 | | z^2=-2 | | 3s+7=41-56 | | 49-4x=14-10x | | z^3=-3 | | Z^4=2i | | 10+6v=104 | | 3Q=4R+39 |

Equations solver categories