4w^2-13w-27=0

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Solution for 4w^2-13w-27=0 equation:


Simplifying
4w2 + -13w + -27 = 0

Reorder the terms:
-27 + -13w + 4w2 = 0

Solving
-27 + -13w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
-6.75 + -3.25w + w2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + -3.25w + 6.75 + w2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + -3.25w + w2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + -3.25w + w2 = 0 + 6.75
-3.25w + w2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
-3.25w + w2 = 6.75

The w term is -3.25w.  Take half its coefficient (-1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
-3.25w + 2.640625 + w2 = 6.75 + 2.640625

Reorder the terms:
2.640625 + -3.25w + w2 = 6.75 + 2.640625

Combine like terms: 6.75 + 2.640625 = 9.390625
2.640625 + -3.25w + w2 = 9.390625

Factor a perfect square on the left side:
(w + -1.625)(w + -1.625) = 9.390625

Calculate the square root of the right side: 3.064412668

Break this problem into two subproblems by setting 
(w + -1.625) equal to 3.064412668 and -3.064412668.

Subproblem 1

w + -1.625 = 3.064412668 Simplifying w + -1.625 = 3.064412668 Reorder the terms: -1.625 + w = 3.064412668 Solving -1.625 + w = 3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = 3.064412668 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = 3.064412668 + 1.625 w = 3.064412668 + 1.625 Combine like terms: 3.064412668 + 1.625 = 4.689412668 w = 4.689412668 Simplifying w = 4.689412668

Subproblem 2

w + -1.625 = -3.064412668 Simplifying w + -1.625 = -3.064412668 Reorder the terms: -1.625 + w = -3.064412668 Solving -1.625 + w = -3.064412668 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + w = -3.064412668 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + w = -3.064412668 + 1.625 w = -3.064412668 + 1.625 Combine like terms: -3.064412668 + 1.625 = -1.439412668 w = -1.439412668 Simplifying w = -1.439412668

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.689412668, -1.439412668}

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