x^2+4x-66=0

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Solution for x^2+4x-66=0 equation: 


Simplifying
x2 + 4x + -66 = 0

Reorder the terms:
-66 + 4x + x2 = 0

Solving
-66 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 4x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 4x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 4x + x2 = 0 + 66
4x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
4x + x2 = 66

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 66 + 4

Reorder the terms:
4 + 4x + x2 = 66 + 4

Combine like terms: 66 + 4 = 70
4 + 4x + x2 = 70

Factor a perfect square on the left side:
(x + 2)(x + 2) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 2) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + 2 = 8.366600265

Simplifying
x + 2 = 8.366600265

Reorder the terms:
2 + x = 8.366600265

Solving
2 + x = 8.366600265

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.366600265 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.366600265 + -2
x = 8.366600265 + -2

Combine like terms: 8.366600265 + -2 = 6.366600265
x = 6.366600265

Simplifying
x = 6.366600265


Subproblem 2
x + 2 = -8.366600265

Simplifying
x + 2 = -8.366600265

Reorder the terms:
2 + x = -8.366600265

Solving
2 + x = -8.366600265

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.366600265 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.366600265 + -2
x = -8.366600265 + -2

Combine like terms: -8.366600265 + -2 = -10.366600265
x = -10.366600265

Simplifying
x = -10.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.366600265, -10.366600265}

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