-25w^2+20w+44=0

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Solution for -25w^2+20w+44=0 equation:


Simplifying
-25w2 + 20w + 44 = 0

Reorder the terms:
44 + 20w + -25w2 = 0

Solving
44 + 20w + -25w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-25 the coefficient of the squared term: 

Divide each side by '-25'.
-1.76 + -0.8w + w2 = 0

Move the constant term to the right:

Add '1.76' to each side of the equation.
-1.76 + -0.8w + 1.76 + w2 = 0 + 1.76

Reorder the terms:
-1.76 + 1.76 + -0.8w + w2 = 0 + 1.76

Combine like terms: -1.76 + 1.76 = 0.00
0.00 + -0.8w + w2 = 0 + 1.76
-0.8w + w2 = 0 + 1.76

Combine like terms: 0 + 1.76 = 1.76
-0.8w + w2 = 1.76

The w term is -0.8w.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8w + 0.16 + w2 = 1.76 + 0.16

Reorder the terms:
0.16 + -0.8w + w2 = 1.76 + 0.16

Combine like terms: 1.76 + 0.16 = 1.92
0.16 + -0.8w + w2 = 1.92

Factor a perfect square on the left side:
(w + -0.4)(w + -0.4) = 1.92

Calculate the square root of the right side: 1.385640646

Break this problem into two subproblems by setting 
(w + -0.4) equal to 1.385640646 and -1.385640646.

Subproblem 1

w + -0.4 = 1.385640646 Simplifying w + -0.4 = 1.385640646 Reorder the terms: -0.4 + w = 1.385640646 Solving -0.4 + w = 1.385640646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = 1.385640646 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = 1.385640646 + 0.4 w = 1.385640646 + 0.4 Combine like terms: 1.385640646 + 0.4 = 1.785640646 w = 1.785640646 Simplifying w = 1.785640646

Subproblem 2

w + -0.4 = -1.385640646 Simplifying w + -0.4 = -1.385640646 Reorder the terms: -0.4 + w = -1.385640646 Solving -0.4 + w = -1.385640646 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + w = -1.385640646 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + w = -1.385640646 + 0.4 w = -1.385640646 + 0.4 Combine like terms: -1.385640646 + 0.4 = -0.985640646 w = -0.985640646 Simplifying w = -0.985640646

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.785640646, -0.985640646}

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