w^2-5w-25=0

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Solution for w^2-5w-25=0 equation:


Simplifying
w2 + -5w + -25 = 0

Reorder the terms:
-25 + -5w + w2 = 0

Solving
-25 + -5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -5w + 25 + w2 = 0 + 25

Reorder the terms:
-25 + 25 + -5w + w2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -5w + w2 = 0 + 25
-5w + w2 = 0 + 25

Combine like terms: 0 + 25 = 25
-5w + w2 = 25

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = 25 + 6.25

Reorder the terms:
6.25 + -5w + w2 = 25 + 6.25

Combine like terms: 25 + 6.25 = 31.25
6.25 + -5w + w2 = 31.25

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 31.25

Calculate the square root of the right side: 5.590169944

Break this problem into two subproblems by setting 
(w + -2.5) equal to 5.590169944 and -5.590169944.

Subproblem 1

w + -2.5 = 5.590169944 Simplifying w + -2.5 = 5.590169944 Reorder the terms: -2.5 + w = 5.590169944 Solving -2.5 + w = 5.590169944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = 5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = 5.590169944 + 2.5 w = 5.590169944 + 2.5 Combine like terms: 5.590169944 + 2.5 = 8.090169944 w = 8.090169944 Simplifying w = 8.090169944

Subproblem 2

w + -2.5 = -5.590169944 Simplifying w + -2.5 = -5.590169944 Reorder the terms: -2.5 + w = -5.590169944 Solving -2.5 + w = -5.590169944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + w = -5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + w = -5.590169944 + 2.5 w = -5.590169944 + 2.5 Combine like terms: -5.590169944 + 2.5 = -3.090169944 w = -3.090169944 Simplifying w = -3.090169944

Solution

The solution to the problem is based on the solutions from the subproblems. w = {8.090169944, -3.090169944}

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