w^2-20w+13=0

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Solution for w^2-20w+13=0 equation:


Simplifying
w2 + -20w + 13 = 0

Reorder the terms:
13 + -20w + w2 = 0

Solving
13 + -20w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -20w + -13 + w2 = 0 + -13

Reorder the terms:
13 + -13 + -20w + w2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -20w + w2 = 0 + -13
-20w + w2 = 0 + -13

Combine like terms: 0 + -13 = -13
-20w + w2 = -13

The w term is -20w.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20w + 100 + w2 = -13 + 100

Reorder the terms:
100 + -20w + w2 = -13 + 100

Combine like terms: -13 + 100 = 87
100 + -20w + w2 = 87

Factor a perfect square on the left side:
(w + -10)(w + -10) = 87

Calculate the square root of the right side: 9.327379053

Break this problem into two subproblems by setting 
(w + -10) equal to 9.327379053 and -9.327379053.

Subproblem 1

w + -10 = 9.327379053 Simplifying w + -10 = 9.327379053 Reorder the terms: -10 + w = 9.327379053 Solving -10 + w = 9.327379053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + w = 9.327379053 + 10 Combine like terms: -10 + 10 = 0 0 + w = 9.327379053 + 10 w = 9.327379053 + 10 Combine like terms: 9.327379053 + 10 = 19.327379053 w = 19.327379053 Simplifying w = 19.327379053

Subproblem 2

w + -10 = -9.327379053 Simplifying w + -10 = -9.327379053 Reorder the terms: -10 + w = -9.327379053 Solving -10 + w = -9.327379053 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + w = -9.327379053 + 10 Combine like terms: -10 + 10 = 0 0 + w = -9.327379053 + 10 w = -9.327379053 + 10 Combine like terms: -9.327379053 + 10 = 0.672620947 w = 0.672620947 Simplifying w = 0.672620947

Solution

The solution to the problem is based on the solutions from the subproblems. w = {19.327379053, 0.672620947}

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