9w^2-50w+56=8w-7

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Solution for 9w^2-50w+56=8w-7 equation:


Simplifying
9w2 + -50w + 56 = 8w + -7

Reorder the terms:
56 + -50w + 9w2 = 8w + -7

Reorder the terms:
56 + -50w + 9w2 = -7 + 8w

Solving
56 + -50w + 9w2 = -7 + 8w

Solving for variable 'w'.

Reorder the terms:
56 + 7 + -50w + -8w + 9w2 = -7 + 8w + 7 + -8w

Combine like terms: 56 + 7 = 63
63 + -50w + -8w + 9w2 = -7 + 8w + 7 + -8w

Combine like terms: -50w + -8w = -58w
63 + -58w + 9w2 = -7 + 8w + 7 + -8w

Reorder the terms:
63 + -58w + 9w2 = -7 + 7 + 8w + -8w

Combine like terms: -7 + 7 = 0
63 + -58w + 9w2 = 0 + 8w + -8w
63 + -58w + 9w2 = 8w + -8w

Combine like terms: 8w + -8w = 0
63 + -58w + 9w2 = 0

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

Divide each side by '9'.
7 + -6.444444444w + w2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6.444444444w + -7 + w2 = 0 + -7

Reorder the terms:
7 + -7 + -6.444444444w + w2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6.444444444w + w2 = 0 + -7
-6.444444444w + w2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6.444444444w + w2 = -7

The w term is -6.444444444w.  Take half its coefficient (-3.222222222).
Square it (10.38271605) and add it to both sides.

Add '10.38271605' to each side of the equation.
-6.444444444w + 10.38271605 + w2 = -7 + 10.38271605

Reorder the terms:
10.38271605 + -6.444444444w + w2 = -7 + 10.38271605

Combine like terms: -7 + 10.38271605 = 3.38271605
10.38271605 + -6.444444444w + w2 = 3.38271605

Factor a perfect square on the left side:
(w + -3.222222222)(w + -3.222222222) = 3.38271605

Calculate the square root of the right side: 1.839216151

Break this problem into two subproblems by setting 
(w + -3.222222222) equal to 1.839216151 and -1.839216151.

Subproblem 1

w + -3.222222222 = 1.839216151 Simplifying w + -3.222222222 = 1.839216151 Reorder the terms: -3.222222222 + w = 1.839216151 Solving -3.222222222 + w = 1.839216151 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + w = 1.839216151 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + w = 1.839216151 + 3.222222222 w = 1.839216151 + 3.222222222 Combine like terms: 1.839216151 + 3.222222222 = 5.061438373 w = 5.061438373 Simplifying w = 5.061438373

Subproblem 2

w + -3.222222222 = -1.839216151 Simplifying w + -3.222222222 = -1.839216151 Reorder the terms: -3.222222222 + w = -1.839216151 Solving -3.222222222 + w = -1.839216151 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + w = -1.839216151 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + w = -1.839216151 + 3.222222222 w = -1.839216151 + 3.222222222 Combine like terms: -1.839216151 + 3.222222222 = 1.383006071 w = 1.383006071 Simplifying w = 1.383006071

Solution

The solution to the problem is based on the solutions from the subproblems. w = {5.061438373, 1.383006071}

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