(10-3w)(w)=77

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Solution for (10-3w)(w)=77 equation: 


Simplifying
(10 + -3w)(w) = 77

Reorder the terms for easier multiplication:
w(10 + -3w) = 77
(10 * w + -3w * w) = 77
(10w + -3w2) = 77

Solving
10w + -3w2 = 77

Solving for variable 'w'.

Reorder the terms:
-77 + 10w + -3w2 = 77 + -77

Combine like terms: 77 + -77 = 0
-77 + 10w + -3w2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
25.66666667 + -3.333333333w + w2 = 0

Move the constant term to the right:

Add '-25.66666667' to each side of the equation.
25.66666667 + -3.333333333w + -25.66666667 + w2 = 0 + -25.66666667

Reorder the terms:
25.66666667 + -25.66666667 + -3.333333333w + w2 = 0 + -25.66666667

Combine like terms: 25.66666667 + -25.66666667 = 0.00000000
0.00000000 + -3.333333333w + w2 = 0 + -25.66666667
-3.333333333w + w2 = 0 + -25.66666667

Combine like terms: 0 + -25.66666667 = -25.66666667
-3.333333333w + w2 = -25.66666667

The w term is -3.333333333w.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333w + 2.777777779 + w2 = -25.66666667 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333w + w2 = -25.66666667 + 2.777777779

Combine like terms: -25.66666667 + 2.777777779 = -22.888888891
2.777777779 + -3.333333333w + w2 = -22.888888891

Factor a perfect square on the left side:
(w + -1.666666667)(w + -1.666666667) = -22.888888891

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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