0.0048650625+0.1395w+w^2=0.0282150625

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Solution for 0.0048650625+0.1395w+w^2=0.0282150625 equation:


Simplifying
0.0048650625 + 0.1395w + w2 = 0.0282150625

Solving
0.0048650625 + 0.1395w + w2 = 0.0282150625

Solving for variable 'w'.

Reorder the terms:
0.0048650625 + -0.0282150625 + 0.1395w + w2 = 0.0282150625 + -0.0282150625

Combine like terms: 0.0048650625 + -0.0282150625 = -0.02335
-0.02335 + 0.1395w + w2 = 0.0282150625 + -0.0282150625

Combine like terms: 0.0282150625 + -0.0282150625 = 0.0000000000
-0.02335 + 0.1395w + w2 = 0.0000000000

Begin completing the square.

Move the constant term to the right:

Add '0.02335' to each side of the equation.
-0.02335 + 0.1395w + 0.02335 + w2 = 0.0000000000 + 0.02335

Reorder the terms:
-0.02335 + 0.02335 + 0.1395w + w2 = 0.0000000000 + 0.02335

Combine like terms: -0.02335 + 0.02335 = 0.00000
0.00000 + 0.1395w + w2 = 0.0000000000 + 0.02335
0.1395w + w2 = 0.0000000000 + 0.02335

Combine like terms: 0.0000000000 + 0.02335 = 0.02335
0.1395w + w2 = 0.02335

The w term is 0.1395w.  Take half its coefficient (0.06975).
Square it (0.0048650625) and add it to both sides.

Add '0.0048650625' to each side of the equation.
0.1395w + 0.0048650625 + w2 = 0.02335 + 0.0048650625

Reorder the terms:
0.0048650625 + 0.1395w + w2 = 0.02335 + 0.0048650625

Combine like terms: 0.02335 + 0.0048650625 = 0.0282150625
0.0048650625 + 0.1395w + w2 = 0.0282150625

Factor a perfect square on the left side:
(w + 0.06975)(w + 0.06975) = 0.0282150625

Calculate the square root of the right side: 0.167973398

Break this problem into two subproblems by setting 
(w + 0.06975) equal to 0.167973398 and -0.167973398.


Subproblem 1
w + 0.06975 = 0.167973398

Simplifying
w + 0.06975 = 0.167973398

Reorder the terms:
0.06975 + w = 0.167973398

Solving
0.06975 + w = 0.167973398

Solving for variable 'w'.

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

Add '-0.06975' to each side of the equation.
0.06975 + -0.06975 + w = 0.167973398 + -0.06975

Combine like terms: 0.06975 + -0.06975 = 0.00000
0.00000 + w = 0.167973398 + -0.06975
w = 0.167973398 + -0.06975

Combine like terms: 0.167973398 + -0.06975 = 0.098223398
w = 0.098223398

Simplifying
w = 0.098223398


Subproblem 2
w + 0.06975 = -0.167973398

Simplifying
w + 0.06975 = -0.167973398

Reorder the terms:
0.06975 + w = -0.167973398

Solving
0.06975 + w = -0.167973398

Solving for variable 'w'.

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

Add '-0.06975' to each side of the equation.
0.06975 + -0.06975 + w = -0.167973398 + -0.06975

Combine like terms: 0.06975 + -0.06975 = 0.00000
0.00000 + w = -0.167973398 + -0.06975
w = -0.167973398 + -0.06975

Combine like terms: -0.167973398 + -0.06975 = -0.237723398
w = -0.237723398

Simplifying
w = -0.237723398


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.098223398, -0.237723398}

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