w^2-6w+9-13=0

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Solution for w^2-6w+9-13=0 equation:


Simplifying
w2 + -6w + 9 + -13 = 0

Reorder the terms:
9 + -13 + -6w + w2 = 0

Combine like terms: 9 + -13 = -4
-4 + -6w + w2 = 0

Solving
-4 + -6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -6w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6w + w2 = 0 + 4
-6w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6w + w2 = 4

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = 4 + 9

Reorder the terms:
9 + -6w + w2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6w + w2 = 13

Factor a perfect square on the left side:
(w + -3)(w + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(w + -3) equal to 3.605551275 and -3.605551275.

Subproblem 1

w + -3 = 3.605551275 Simplifying w + -3 = 3.605551275 Reorder the terms: -3 + w = 3.605551275 Solving -3 + w = 3.605551275 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + w = 3.605551275 + 3 w = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 w = 6.605551275 Simplifying w = 6.605551275

Subproblem 2

w + -3 = -3.605551275 Simplifying w + -3 = -3.605551275 Reorder the terms: -3 + w = -3.605551275 Solving -3 + w = -3.605551275 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + w = -3.605551275 + 3 w = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 w = -0.605551275 Simplifying w = -0.605551275

Solution

The solution to the problem is based on the solutions from the subproblems. w = {6.605551275, -0.605551275}

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