w^2-30w-48=0

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Solution for w^2-30w-48=0 equation: 


Simplifying
w2 + -30w + -48 = 0

Reorder the terms:
-48 + -30w + w2 = 0

Solving
-48 + -30w + 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 + -30w + 48 + w2 = 0 + 48

Reorder the terms:
-48 + 48 + -30w + w2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -30w + w2 = 0 + 48
-30w + w2 = 0 + 48

Combine like terms: 0 + 48 = 48
-30w + w2 = 48

The w term is -30w.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30w + 225 + w2 = 48 + 225

Reorder the terms:
225 + -30w + w2 = 48 + 225

Combine like terms: 48 + 225 = 273
225 + -30w + w2 = 273

Factor a perfect square on the left side:
(w + -15)(w + -15) = 273

Calculate the square root of the right side: 16.522711642

Break this problem into two subproblems by setting 
(w + -15) equal to 16.522711642 and -16.522711642.


Subproblem 1
w + -15 = 16.522711642

Simplifying
w + -15 = 16.522711642

Reorder the terms:
-15 + w = 16.522711642

Solving
-15 + w = 16.522711642

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + w = 16.522711642 + 15

Combine like terms: -15 + 15 = 0
0 + w = 16.522711642 + 15
w = 16.522711642 + 15

Combine like terms: 16.522711642 + 15 = 31.522711642
w = 31.522711642

Simplifying
w = 31.522711642


Subproblem 2
w + -15 = -16.522711642

Simplifying
w + -15 = -16.522711642

Reorder the terms:
-15 + w = -16.522711642

Solving
-15 + w = -16.522711642

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '15' to each side of the equation.
-15 + 15 + w = -16.522711642 + 15

Combine like terms: -15 + 15 = 0
0 + w = -16.522711642 + 15
w = -16.522711642 + 15

Combine like terms: -16.522711642 + 15 = -1.522711642
w = -1.522711642

Simplifying
w = -1.522711642


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {31.522711642, -1.522711642}

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