w(w-6)=80

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Solution for w(w-6)=80 equation:


Simplifying
w(w + -6) = 80

Reorder the terms:
w(-6 + w) = 80
(-6 * w + w * w) = 80
(-6w + w2) = 80

Solving
-6w + w2 = 80

Solving for variable 'w'.

Reorder the terms:
-80 + -6w + w2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -6w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -6w + 80 + w2 = 0 + 80

Reorder the terms:
-80 + 80 + -6w + w2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -6w + w2 = 0 + 80
-6w + w2 = 0 + 80

Combine like terms: 0 + 80 = 80
-6w + w2 = 80

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 = 80 + 9

Reorder the terms:
9 + -6w + w2 = 80 + 9

Combine like terms: 80 + 9 = 89
9 + -6w + w2 = 89

Factor a perfect square on the left side:
(w + -3)(w + -3) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(w + -3) equal to 9.433981132 and -9.433981132.

Subproblem 1

w + -3 = 9.433981132 Simplifying w + -3 = 9.433981132 Reorder the terms: -3 + w = 9.433981132 Solving -3 + w = 9.433981132 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 = 9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + w = 9.433981132 + 3 w = 9.433981132 + 3 Combine like terms: 9.433981132 + 3 = 12.433981132 w = 12.433981132 Simplifying w = 12.433981132

Subproblem 2

w + -3 = -9.433981132 Simplifying w + -3 = -9.433981132 Reorder the terms: -3 + w = -9.433981132 Solving -3 + w = -9.433981132 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 = -9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + w = -9.433981132 + 3 w = -9.433981132 + 3 Combine like terms: -9.433981132 + 3 = -6.433981132 w = -6.433981132 Simplifying w = -6.433981132

Solution

The solution to the problem is based on the solutions from the subproblems. w = {12.433981132, -6.433981132}

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