2w^2+2w-48=0

Simple and best practice solution for 2w^2+2w-48=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 2w^2+2w-48=0 equation:


Simplifying
2w2 + 2w + -48 = 0

Reorder the terms:
-48 + 2w + 2w2 = 0

Solving
-48 + 2w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-24 + w + w2)' equal to zero and attempt to solve:

Simplifying
-24 + w + w2 = 0

Solving
-24 + w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + w + 24 + w2 = 0 + 24

Reorder the terms:
-24 + 24 + w + w2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + w + w2 = 0 + 24
w + w2 = 0 + 24

Combine like terms: 0 + 24 = 24
w + w2 = 24

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 24 + 0.25

Reorder the terms:
0.25 + w + w2 = 24 + 0.25

Combine like terms: 24 + 0.25 = 24.25
0.25 + w + w2 = 24.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(w + 0.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
w + 0.5 = 4.924428901

Simplifying
w + 0.5 = 4.924428901

Reorder the terms:
0.5 + w = 4.924428901

Solving
0.5 + w = 4.924428901

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 4.924428901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 4.924428901 + -0.5
w = 4.924428901 + -0.5

Combine like terms: 4.924428901 + -0.5 = 4.424428901
w = 4.424428901

Simplifying
w = 4.424428901


Subproblem 2
w + 0.5 = -4.924428901

Simplifying
w + 0.5 = -4.924428901

Reorder the terms:
0.5 + w = -4.924428901

Solving
0.5 + w = -4.924428901

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -4.924428901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -4.924428901 + -0.5
w = -4.924428901 + -0.5

Combine like terms: -4.924428901 + -0.5 = -5.424428901
w = -5.424428901

Simplifying
w = -5.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.424428901, -5.424428901}
Solution
w = {4.424428901, -5.424428901}

See similar equations:

| a^2+13a+36=0 | | 5r-2r^2=0 | | 5-x=3x+5 | | 35n^2-6n-8=0 | | 3z^2-12z=0 | | y=55x | | 12v^2-75= | | 7(x+5)=9(x+3) | | -y^2=22y+121 | | r+2r-33=0 | | 15x+5y=10 | | 2(x-4)+4=2x-4(4-x) | | 5(3x-7)-4=5(x-3)+16 | | m^2-8m=0 | | -4x-21=-x^2 | | 70=x(20)/x+20 | | (7x+2)+(-8x+8)= | | 3x^2=2x+3 | | x^3+7x^2-44x=0 | | n-10n+24=0 | | m^3+3m^2=18m | | 4y^2-16Y+16= | | 9x^2-7x+108=0 | | a^2-16a=-64 | | (y-2)(y-3)=9y+6 | | 4k^2-16=0 | | t^2+t-30=0 | | 5k^2=2k+18 | | (2b+7)(b-7)=0 | | 12x^2+29x-5=3 | | 3t^2-4t=0 | | a^2=121 |

Equations solver categories