x^2+33x-100=7

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Solution for x^2+33x-100=7 equation:


Simplifying
x2 + 33x + -100 = 7

Reorder the terms:
-100 + 33x + x2 = 7

Solving
-100 + 33x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-100 + -7 + 33x + x2 = 7 + -7

Combine like terms: -100 + -7 = -107
-107 + 33x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-107 + 33x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '107' to each side of the equation.
-107 + 33x + 107 + x2 = 0 + 107

Reorder the terms:
-107 + 107 + 33x + x2 = 0 + 107

Combine like terms: -107 + 107 = 0
0 + 33x + x2 = 0 + 107
33x + x2 = 0 + 107

Combine like terms: 0 + 107 = 107
33x + x2 = 107

The x term is 33x.  Take half its coefficient (16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
33x + 272.25 + x2 = 107 + 272.25

Reorder the terms:
272.25 + 33x + x2 = 107 + 272.25

Combine like terms: 107 + 272.25 = 379.25
272.25 + 33x + x2 = 379.25

Factor a perfect square on the left side:
(x + 16.5)(x + 16.5) = 379.25

Calculate the square root of the right side: 19.474342094

Break this problem into two subproblems by setting 
(x + 16.5) equal to 19.474342094 and -19.474342094.


Subproblem 1
x + 16.5 = 19.474342094

Simplifying
x + 16.5 = 19.474342094

Reorder the terms:
16.5 + x = 19.474342094

Solving
16.5 + x = 19.474342094

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = 19.474342094 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = 19.474342094 + -16.5
x = 19.474342094 + -16.5

Combine like terms: 19.474342094 + -16.5 = 2.974342094
x = 2.974342094

Simplifying
x = 2.974342094


Subproblem 2
x + 16.5 = -19.474342094

Simplifying
x + 16.5 = -19.474342094

Reorder the terms:
16.5 + x = -19.474342094

Solving
16.5 + x = -19.474342094

Solving for variable 'x'.

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

Add '-16.5' to each side of the equation.
16.5 + -16.5 + x = -19.474342094 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + x = -19.474342094 + -16.5
x = -19.474342094 + -16.5

Combine like terms: -19.474342094 + -16.5 = -35.974342094
x = -35.974342094

Simplifying
x = -35.974342094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.974342094, -35.974342094}

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