4w^2-112w+425=0

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Solution for 4w^2-112w+425=0 equation:


Simplifying
4w2 + -112w + 425 = 0

Reorder the terms:
425 + -112w + 4w2 = 0

Solving
425 + -112w + 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'.
106.25 + -28w + w2 = 0

Move the constant term to the right:

Add '-106.25' to each side of the equation.
106.25 + -28w + -106.25 + w2 = 0 + -106.25

Reorder the terms:
106.25 + -106.25 + -28w + w2 = 0 + -106.25

Combine like terms: 106.25 + -106.25 = 0.00
0.00 + -28w + w2 = 0 + -106.25
-28w + w2 = 0 + -106.25

Combine like terms: 0 + -106.25 = -106.25
-28w + w2 = -106.25

The w term is -28w.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28w + 196 + w2 = -106.25 + 196

Reorder the terms:
196 + -28w + w2 = -106.25 + 196

Combine like terms: -106.25 + 196 = 89.75
196 + -28w + w2 = 89.75

Factor a perfect square on the left side:
(w + -14)(w + -14) = 89.75

Calculate the square root of the right side: 9.473647661

Break this problem into two subproblems by setting 
(w + -14) equal to 9.473647661 and -9.473647661.

Subproblem 1

w + -14 = 9.473647661 Simplifying w + -14 = 9.473647661 Reorder the terms: -14 + w = 9.473647661 Solving -14 + w = 9.473647661 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = 9.473647661 + 14 Combine like terms: -14 + 14 = 0 0 + w = 9.473647661 + 14 w = 9.473647661 + 14 Combine like terms: 9.473647661 + 14 = 23.473647661 w = 23.473647661 Simplifying w = 23.473647661

Subproblem 2

w + -14 = -9.473647661 Simplifying w + -14 = -9.473647661 Reorder the terms: -14 + w = -9.473647661 Solving -14 + w = -9.473647661 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + w = -9.473647661 + 14 Combine like terms: -14 + 14 = 0 0 + w = -9.473647661 + 14 w = -9.473647661 + 14 Combine like terms: -9.473647661 + 14 = 4.526352339 w = 4.526352339 Simplifying w = 4.526352339

Solution

The solution to the problem is based on the solutions from the subproblems. w = {23.473647661, 4.526352339}

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