w^2+2w=47

Simple and best practice solution for w^2+2w=47 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 w^2+2w=47 equation:


Simplifying
w2 + 2w = 47

Reorder the terms:
2w + w2 = 47

Solving
2w + w2 = 47

Solving for variable 'w'.

Reorder the terms:
-47 + 2w + w2 = 47 + -47

Combine like terms: 47 + -47 = 0
-47 + 2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + 2w + 47 + w2 = 0 + 47

Reorder the terms:
-47 + 47 + 2w + w2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + 2w + w2 = 0 + 47
2w + w2 = 0 + 47

Combine like terms: 0 + 47 = 47
2w + w2 = 47

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 47 + 1

Reorder the terms:
1 + 2w + w2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + 2w + w2 = 48

Factor a perfect square on the left side:
(w + 1)(w + 1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(w + 1) equal to 6.92820323 and -6.92820323.

Subproblem 1

w + 1 = 6.92820323 Simplifying w + 1 = 6.92820323 Reorder the terms: 1 + w = 6.92820323 Solving 1 + w = 6.92820323 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + w = 6.92820323 + -1 w = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 w = 5.92820323 Simplifying w = 5.92820323

Subproblem 2

w + 1 = -6.92820323 Simplifying w + 1 = -6.92820323 Reorder the terms: 1 + w = -6.92820323 Solving 1 + w = -6.92820323 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + w = -6.92820323 + -1 w = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 w = -7.92820323 Simplifying w = -7.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. w = {5.92820323, -7.92820323}

See similar equations:

| 4.5+8.2+3.5x=-4.6+8x | | 2[y-3]=y+4 | | -10x-5y=-30 | | 5x-15x+10=5x | | -3=6-4r+3 | | 6x+23=5x+36 | | w^2+22w=43 | | q^2+12q+25=0 | | 2x-2=x-3+(5+x) | | 10x-21=4x+15 | | -67+21= | | 10x+11y=92 | | 7*c=21 | | h^2+6h-11=0 | | f^2-10f=33 | | 4x+2+8=35 | | F(X)=8x^2+8-12 | | 2s^2+3s^2+2s+1=0 | | -6m=5 | | 49.5*9= | | 5x-3=13x-24 | | 3x+1.5+x+180=455 | | -18=4b+5b | | 5[2p-4(p+5)]=26 | | -8+2x=4x+5 | | 9x=26-4 | | 6m+m-4(-2m+1-m)=-8 | | 10-7x=35 | | 47.1=10a+30b | | p^2+4p=31 | | 15b+8=9b | | 3(2x+1)=7(X-3) |

Equations solver categories