w^2+4w-6=0

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Solution for w^2+4w-6=0 equation:


Simplifying
w2 + 4w + -6 = 0

Reorder the terms:
-6 + 4w + w2 = 0

Solving
-6 + 4w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4w + 6 + w2 = 0 + 6

Reorder the terms:
-6 + 6 + 4w + w2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4w + w2 = 0 + 6
4w + w2 = 0 + 6

Combine like terms: 0 + 6 = 6
4w + w2 = 6

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 = 6 + 4

Reorder the terms:
4 + 4w + w2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4w + w2 = 10

Factor a perfect square on the left side:
(w + 2)(w + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(w + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1

w + 2 = 3.16227766 Simplifying w + 2 = 3.16227766 Reorder the terms: 2 + w = 3.16227766 Solving 2 + w = 3.16227766 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 = 3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + w = 3.16227766 + -2 w = 3.16227766 + -2 Combine like terms: 3.16227766 + -2 = 1.16227766 w = 1.16227766 Simplifying w = 1.16227766

Subproblem 2

w + 2 = -3.16227766 Simplifying w + 2 = -3.16227766 Reorder the terms: 2 + w = -3.16227766 Solving 2 + w = -3.16227766 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 = -3.16227766 + -2 Combine like terms: 2 + -2 = 0 0 + w = -3.16227766 + -2 w = -3.16227766 + -2 Combine like terms: -3.16227766 + -2 = -5.16227766 w = -5.16227766 Simplifying w = -5.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. w = {1.16227766, -5.16227766}

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