1w^2+2w-312=0

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Solution for 1w^2+2w-312=0 equation:


Simplifying
1w2 + 2w + -312 = 0

Reorder the terms:
-312 + 2w + 1w2 = 0

Solving
-312 + 2w + 1w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '312' to each side of the equation.
-312 + 2w + 312 + w2 = 0 + 312

Reorder the terms:
-312 + 312 + 2w + w2 = 0 + 312

Combine like terms: -312 + 312 = 0
0 + 2w + w2 = 0 + 312
2w + w2 = 0 + 312

Combine like terms: 0 + 312 = 312
2w + w2 = 312

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 312 + 1

Reorder the terms:
1 + 2w + w2 = 312 + 1

Combine like terms: 312 + 1 = 313
1 + 2w + w2 = 313

Factor a perfect square on the left side:
(w + 1)(w + 1) = 313

Calculate the square root of the right side: 17.691806013

Break this problem into two subproblems by setting 
(w + 1) equal to 17.691806013 and -17.691806013.

Subproblem 1

w + 1 = 17.691806013 Simplifying w + 1 = 17.691806013 Reorder the terms: 1 + w = 17.691806013 Solving 1 + w = 17.691806013 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 17.691806013 + -1 Combine like terms: 1 + -1 = 0 0 + w = 17.691806013 + -1 w = 17.691806013 + -1 Combine like terms: 17.691806013 + -1 = 16.691806013 w = 16.691806013 Simplifying w = 16.691806013

Subproblem 2

w + 1 = -17.691806013 Simplifying w + 1 = -17.691806013 Reorder the terms: 1 + w = -17.691806013 Solving 1 + w = -17.691806013 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -17.691806013 + -1 Combine like terms: 1 + -1 = 0 0 + w = -17.691806013 + -1 w = -17.691806013 + -1 Combine like terms: -17.691806013 + -1 = -18.691806013 w = -18.691806013 Simplifying w = -18.691806013

Solution

The solution to the problem is based on the solutions from the subproblems. w = {16.691806013, -18.691806013}

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