x^2+42x-200=0

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Solution for x^2+42x-200=0 equation: 


Simplifying
x2 + 42x + -200 = 0

Reorder the terms:
-200 + 42x + x2 = 0

Solving
-200 + 42x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 42x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 42x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 42x + x2 = 0 + 200
42x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
42x + x2 = 200

The x term is 42x.  Take half its coefficient (21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
42x + 441 + x2 = 200 + 441

Reorder the terms:
441 + 42x + x2 = 200 + 441

Combine like terms: 200 + 441 = 641
441 + 42x + x2 = 641

Factor a perfect square on the left side:
(x + 21)(x + 21) = 641

Calculate the square root of the right side: 25.317977802

Break this problem into two subproblems by setting 
(x + 21) equal to 25.317977802 and -25.317977802.


Subproblem 1
x + 21 = 25.317977802

Simplifying
x + 21 = 25.317977802

Reorder the terms:
21 + x = 25.317977802

Solving
21 + x = 25.317977802

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = 25.317977802 + -21

Combine like terms: 21 + -21 = 0
0 + x = 25.317977802 + -21
x = 25.317977802 + -21

Combine like terms: 25.317977802 + -21 = 4.317977802
x = 4.317977802

Simplifying
x = 4.317977802


Subproblem 2
x + 21 = -25.317977802

Simplifying
x + 21 = -25.317977802

Reorder the terms:
21 + x = -25.317977802

Solving
21 + x = -25.317977802

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = -25.317977802 + -21

Combine like terms: 21 + -21 = 0
0 + x = -25.317977802 + -21
x = -25.317977802 + -21

Combine like terms: -25.317977802 + -21 = -46.317977802
x = -46.317977802

Simplifying
x = -46.317977802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.317977802, -46.317977802}

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