0=4w^2-5w-36

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Solution for 0=4w^2-5w-36 equation:


Simplifying
0 = 4w2 + -5w + -36

Reorder the terms:
0 = -36 + -5w + 4w2

Solving
0 = -36 + -5w + 4w2

Solving for variable 'w'.

Combine like terms: 0 + 36 = 36
36 + 5w + -4w2 = -36 + -5w + 4w2 + 36 + 5w + -4w2

Reorder the terms:
36 + 5w + -4w2 = -36 + 36 + -5w + 5w + 4w2 + -4w2

Combine like terms: -36 + 36 = 0
36 + 5w + -4w2 = 0 + -5w + 5w + 4w2 + -4w2
36 + 5w + -4w2 = -5w + 5w + 4w2 + -4w2

Combine like terms: -5w + 5w = 0
36 + 5w + -4w2 = 0 + 4w2 + -4w2
36 + 5w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
36 + 5w + -4w2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-9 + -1.25w + w2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1.25w + 9 + w2 = 0 + 9

Reorder the terms:
-9 + 9 + -1.25w + w2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1.25w + w2 = 0 + 9
-1.25w + w2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1.25w + w2 = 9

The w term is -1.25w.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25w + 0.390625 + w2 = 9 + 0.390625

Reorder the terms:
0.390625 + -1.25w + w2 = 9 + 0.390625

Combine like terms: 9 + 0.390625 = 9.390625
0.390625 + -1.25w + w2 = 9.390625

Factor a perfect square on the left side:
(w + -0.625)(w + -0.625) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(w + -0.625) equal to 3.064412668 and -3.064412668.

Subproblem 1

w + -0.625 = 3.064412668 Simplifying w + -0.625 = 3.064412668 Reorder the terms: -0.625 + w = 3.064412668 Solving -0.625 + w = 3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = 3.064412668 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = 3.064412668 + 0.625 w = 3.064412668 + 0.625 Combine like terms: 3.064412668 + 0.625 = 3.689412668 w = 3.689412668 Simplifying w = 3.689412668

Subproblem 2

w + -0.625 = -3.064412668 Simplifying w + -0.625 = -3.064412668 Reorder the terms: -0.625 + w = -3.064412668 Solving -0.625 + w = -3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + w = -3.064412668 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + w = -3.064412668 + 0.625 w = -3.064412668 + 0.625 Combine like terms: -3.064412668 + 0.625 = -2.439412668 w = -2.439412668 Simplifying w = -2.439412668

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.689412668, -2.439412668}

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