x^2+88x-300=0

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Solution for x^2+88x-300=0 equation: 


Simplifying
x2 + 88x + -300 = 0

Reorder the terms:
-300 + 88x + x2 = 0

Solving
-300 + 88x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 88x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 88x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 88x + x2 = 0 + 300
88x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
88x + x2 = 300

The x term is 88x.  Take half its coefficient (44).
Square it (1936) and add it to both sides.

Add '1936' to each side of the equation.
88x + 1936 + x2 = 300 + 1936

Reorder the terms:
1936 + 88x + x2 = 300 + 1936

Combine like terms: 300 + 1936 = 2236
1936 + 88x + x2 = 2236

Factor a perfect square on the left side:
(x + 44)(x + 44) = 2236

Calculate the square root of the right side: 47.28636167

Break this problem into two subproblems by setting 
(x + 44) equal to 47.28636167 and -47.28636167.


Subproblem 1
x + 44 = 47.28636167

Simplifying
x + 44 = 47.28636167

Reorder the terms:
44 + x = 47.28636167

Solving
44 + x = 47.28636167

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = 47.28636167 + -44

Combine like terms: 44 + -44 = 0
0 + x = 47.28636167 + -44
x = 47.28636167 + -44

Combine like terms: 47.28636167 + -44 = 3.28636167
x = 3.28636167

Simplifying
x = 3.28636167


Subproblem 2
x + 44 = -47.28636167

Simplifying
x + 44 = -47.28636167

Reorder the terms:
44 + x = -47.28636167

Solving
44 + x = -47.28636167

Solving for variable 'x'.

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

Add '-44' to each side of the equation.
44 + -44 + x = -47.28636167 + -44

Combine like terms: 44 + -44 = 0
0 + x = -47.28636167 + -44
x = -47.28636167 + -44

Combine like terms: -47.28636167 + -44 = -91.28636167
x = -91.28636167

Simplifying
x = -91.28636167


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.28636167, -91.28636167}

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