3X^2+20X-1775=0

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Solution for 3X^2+20X-1775=0 equation: 


Simplifying
3X2 + 20X + -1775 = 0

Reorder the terms:
-1775 + 20X + 3X2 = 0

Solving
-1775 + 20X + 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'.
-591.6666667 + 6.666666667X + X2 = 0

Move the constant term to the right:

Add '591.6666667' to each side of the equation.
-591.6666667 + 6.666666667X + 591.6666667 + X2 = 0 + 591.6666667

Reorder the terms:
-591.6666667 + 591.6666667 + 6.666666667X + X2 = 0 + 591.6666667

Combine like terms: -591.6666667 + 591.6666667 = 0.0000000
0.0000000 + 6.666666667X + X2 = 0 + 591.6666667
6.666666667X + X2 = 0 + 591.6666667

Combine like terms: 0 + 591.6666667 = 591.6666667
6.666666667X + X2 = 591.6666667

The X term is 6.666666667X.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667X + 11.11111112 + X2 = 591.6666667 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667X + X2 = 591.6666667 + 11.11111112

Combine like terms: 591.6666667 + 11.11111112 = 602.77777782
11.11111112 + 6.666666667X + X2 = 602.77777782

Factor a perfect square on the left side:
(X + 3.333333334)(X + 3.333333334) = 602.77777782

Calculate the square root of the right side: 24.551533105

Break this problem into two subproblems by setting 
(X + 3.333333334) equal to 24.551533105 and -24.551533105.


Subproblem 1
X + 3.333333334 = 24.551533105

Simplifying
X + 3.333333334 = 24.551533105

Reorder the terms:
3.333333334 + X = 24.551533105

Solving
3.333333334 + X = 24.551533105

Solving for variable 'X'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + X = 24.551533105 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + X = 24.551533105 + -3.333333334
X = 24.551533105 + -3.333333334

Combine like terms: 24.551533105 + -3.333333334 = 21.218199771
X = 21.218199771

Simplifying
X = 21.218199771


Subproblem 2
X + 3.333333334 = -24.551533105

Simplifying
X + 3.333333334 = -24.551533105

Reorder the terms:
3.333333334 + X = -24.551533105

Solving
3.333333334 + X = -24.551533105

Solving for variable 'X'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + X = -24.551533105 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + X = -24.551533105 + -3.333333334
X = -24.551533105 + -3.333333334

Combine like terms: -24.551533105 + -3.333333334 = -27.884866439
X = -27.884866439

Simplifying
X = -27.884866439


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {21.218199771, -27.884866439}

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