w^2+10w-3=0

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Solution for w^2+10w-3=0 equation:


Simplifying
w2 + 10w + -3 = 0

Reorder the terms:
-3 + 10w + w2 = 0

Solving
-3 + 10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 10w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + 10w + w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 10w + w2 = 0 + 3
10w + w2 = 0 + 3

Combine like terms: 0 + 3 = 3
10w + w2 = 3

The w term is 10w.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10w + 25 + w2 = 3 + 25

Reorder the terms:
25 + 10w + w2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + 10w + w2 = 28

Factor a perfect square on the left side:
(w + 5)(w + 5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(w + 5) equal to 5.291502622 and -5.291502622.

Subproblem 1

w + 5 = 5.291502622 Simplifying w + 5 = 5.291502622 Reorder the terms: 5 + w = 5.291502622 Solving 5 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + w = 5.291502622 + -5 w = 5.291502622 + -5 Combine like terms: 5.291502622 + -5 = 0.291502622 w = 0.291502622 Simplifying w = 0.291502622

Subproblem 2

w + 5 = -5.291502622 Simplifying w + 5 = -5.291502622 Reorder the terms: 5 + w = -5.291502622 Solving 5 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -5.291502622 + -5 Combine like terms: 5 + -5 = 0 0 + w = -5.291502622 + -5 w = -5.291502622 + -5 Combine like terms: -5.291502622 + -5 = -10.291502622 w = -10.291502622 Simplifying w = -10.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.291502622, -10.291502622}

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