3x^2+62x-200=0

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Solution for 3x^2+62x-200=0 equation: 


Simplifying
3x2 + 62x + -200 = 0

Reorder the terms:
-200 + 62x + 3x2 = 0

Solving
-200 + 62x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-66.66666667 + 20.66666667x + x2 = 0

Move the constant term to the right:

Add '66.66666667' to each side of the equation.
-66.66666667 + 20.66666667x + 66.66666667 + x2 = 0 + 66.66666667

Reorder the terms:
-66.66666667 + 66.66666667 + 20.66666667x + x2 = 0 + 66.66666667

Combine like terms: -66.66666667 + 66.66666667 = 0.00000000
0.00000000 + 20.66666667x + x2 = 0 + 66.66666667
20.66666667x + x2 = 0 + 66.66666667

Combine like terms: 0 + 66.66666667 = 66.66666667
20.66666667x + x2 = 66.66666667

The x term is 20.66666667x.  Take half its coefficient (10.33333334).
Square it (106.7777779) and add it to both sides.

Add '106.7777779' to each side of the equation.
20.66666667x + 106.7777779 + x2 = 66.66666667 + 106.7777779

Reorder the terms:
106.7777779 + 20.66666667x + x2 = 66.66666667 + 106.7777779

Combine like terms: 66.66666667 + 106.7777779 = 173.44444457
106.7777779 + 20.66666667x + x2 = 173.44444457

Factor a perfect square on the left side:
(x + 10.33333334)(x + 10.33333334) = 173.44444457

Calculate the square root of the right side: 13.169830848

Break this problem into two subproblems by setting 
(x + 10.33333334) equal to 13.169830848 and -13.169830848.


Subproblem 1
x + 10.33333334 = 13.169830848

Simplifying
x + 10.33333334 = 13.169830848

Reorder the terms:
10.33333334 + x = 13.169830848

Solving
10.33333334 + x = 13.169830848

Solving for variable 'x'.

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

Add '-10.33333334' to each side of the equation.
10.33333334 + -10.33333334 + x = 13.169830848 + -10.33333334

Combine like terms: 10.33333334 + -10.33333334 = 0.00000000
0.00000000 + x = 13.169830848 + -10.33333334
x = 13.169830848 + -10.33333334

Combine like terms: 13.169830848 + -10.33333334 = 2.836497508
x = 2.836497508

Simplifying
x = 2.836497508


Subproblem 2
x + 10.33333334 = -13.169830848

Simplifying
x + 10.33333334 = -13.169830848

Reorder the terms:
10.33333334 + x = -13.169830848

Solving
10.33333334 + x = -13.169830848

Solving for variable 'x'.

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

Add '-10.33333334' to each side of the equation.
10.33333334 + -10.33333334 + x = -13.169830848 + -10.33333334

Combine like terms: 10.33333334 + -10.33333334 = 0.00000000
0.00000000 + x = -13.169830848 + -10.33333334
x = -13.169830848 + -10.33333334

Combine like terms: -13.169830848 + -10.33333334 = -23.503164188
x = -23.503164188

Simplifying
x = -23.503164188


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.836497508, -23.503164188}

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