2w^2-5w-12.5=0

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Solution for 2w^2-5w-12.5=0 equation:


Simplifying
2w2 + -5w + -12.5 = 0

Reorder the terms:
-12.5 + -5w + 2w2 = 0

Solving
-12.5 + -5w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-6.25 + -2.5w + w2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -2.5w + 6.25 + w2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -2.5w + w2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -2.5w + w2 = 0 + 6.25
-2.5w + w2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-2.5w + w2 = 6.25

The w term is -2.5w.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5w + 1.5625 + w2 = 6.25 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 6.25 + 1.5625

Combine like terms: 6.25 + 1.5625 = 7.8125
1.5625 + -2.5w + w2 = 7.8125

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(w + -1.25) equal to 2.795084972 and -2.795084972.

Subproblem 1

w + -1.25 = 2.795084972 Simplifying w + -1.25 = 2.795084972 Reorder the terms: -1.25 + w = 2.795084972 Solving -1.25 + w = 2.795084972 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = 2.795084972 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 2.795084972 + 1.25 w = 2.795084972 + 1.25 Combine like terms: 2.795084972 + 1.25 = 4.045084972 w = 4.045084972 Simplifying w = 4.045084972

Subproblem 2

w + -1.25 = -2.795084972 Simplifying w + -1.25 = -2.795084972 Reorder the terms: -1.25 + w = -2.795084972 Solving -1.25 + w = -2.795084972 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + w = -2.795084972 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -2.795084972 + 1.25 w = -2.795084972 + 1.25 Combine like terms: -2.795084972 + 1.25 = -1.545084972 w = -1.545084972 Simplifying w = -1.545084972

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.045084972, -1.545084972}

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