2w^2+5=8w

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Solution for 2w^2+5=8w equation:


Simplifying
2w2 + 5 = 8w

Reorder the terms:
5 + 2w2 = 8w

Solving
5 + 2w2 = 8w

Solving for variable 'w'.

Reorder the terms:
5 + -8w + 2w2 = 8w + -8w

Combine like terms: 8w + -8w = 0
5 + -8w + 2w2 = 0

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

Divide each side by '2'.
2.5 + -4w + w2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4w + -2.5 + w2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4w + w2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4w + w2 = 0 + -2.5
-4w + w2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4w + w2 = -2.5

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = -2.5 + 4

Reorder the terms:
4 + -4w + w2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + -4w + w2 = 1.5

Factor a perfect square on the left side:
(w + -2)(w + -2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(w + -2) equal to 1.224744871 and -1.224744871.

Subproblem 1

w + -2 = 1.224744871 Simplifying w + -2 = 1.224744871 Reorder the terms: -2 + w = 1.224744871 Solving -2 + w = 1.224744871 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 1.224744871 + 2 Combine like terms: -2 + 2 = 0 0 + w = 1.224744871 + 2 w = 1.224744871 + 2 Combine like terms: 1.224744871 + 2 = 3.224744871 w = 3.224744871 Simplifying w = 3.224744871

Subproblem 2

w + -2 = -1.224744871 Simplifying w + -2 = -1.224744871 Reorder the terms: -2 + w = -1.224744871 Solving -2 + w = -1.224744871 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -1.224744871 + 2 Combine like terms: -2 + 2 = 0 0 + w = -1.224744871 + 2 w = -1.224744871 + 2 Combine like terms: -1.224744871 + 2 = 0.775255129 w = 0.775255129 Simplifying w = 0.775255129

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.224744871, 0.775255129}

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