w^2+10w-48=0

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Solution for w^2+10w-48=0 equation:


Simplifying
w2 + 10w + -48 = 0

Reorder the terms:
-48 + 10w + w2 = 0

Solving
-48 + 10w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 10w + 48 + w2 = 0 + 48

Reorder the terms:
-48 + 48 + 10w + w2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 10w + w2 = 0 + 48
10w + w2 = 0 + 48

Combine like terms: 0 + 48 = 48
10w + w2 = 48

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 = 48 + 25

Reorder the terms:
25 + 10w + w2 = 48 + 25

Combine like terms: 48 + 25 = 73
25 + 10w + w2 = 73

Factor a perfect square on the left side:
(w + 5)(w + 5) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(w + 5) equal to 8.544003745 and -8.544003745.

Subproblem 1

w + 5 = 8.544003745 Simplifying w + 5 = 8.544003745 Reorder the terms: 5 + w = 8.544003745 Solving 5 + w = 8.544003745 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 = 8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + w = 8.544003745 + -5 w = 8.544003745 + -5 Combine like terms: 8.544003745 + -5 = 3.544003745 w = 3.544003745 Simplifying w = 3.544003745

Subproblem 2

w + 5 = -8.544003745 Simplifying w + 5 = -8.544003745 Reorder the terms: 5 + w = -8.544003745 Solving 5 + w = -8.544003745 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 = -8.544003745 + -5 Combine like terms: 5 + -5 = 0 0 + w = -8.544003745 + -5 w = -8.544003745 + -5 Combine like terms: -8.544003745 + -5 = -13.544003745 w = -13.544003745 Simplifying w = -13.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.544003745, -13.544003745}

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