30x^2-400x-1000=0

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Solution for 30x^2-400x-1000=0 equation: 


Simplifying
30x2 + -400x + -1000 = 0

Reorder the terms:
-1000 + -400x + 30x2 = 0

Solving
-1000 + -400x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-100 + -40x + 3x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-100 + -40x + 3x2)' equal to zero and attempt to solve:

Simplifying
-100 + -40x + 3x2 = 0

Solving
-100 + -40x + 3x2 = 0

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

Divide each side by '3'.
-33.33333333 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + -13.33333333x + 33.33333333 + x2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + -13.33333333x + x2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + 33.33333333
-13.33333333x + x2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
-13.33333333x + x2 = 33.33333333

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = 33.33333333 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = 33.33333333 + 44.44444442

Combine like terms: 33.33333333 + 44.44444442 = 77.77777775
44.44444442 + -13.33333333x + x2 = 77.77777775

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 77.77777775

Calculate the square root of the right side: 8.819171035

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 8.819171035 and -8.819171035.


Subproblem 1
x + -6.666666665 = 8.819171035

Simplifying
x + -6.666666665 = 8.819171035

Reorder the terms:
-6.666666665 + x = 8.819171035

Solving
-6.666666665 + x = 8.819171035

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 8.819171035 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 8.819171035 + 6.666666665
x = 8.819171035 + 6.666666665

Combine like terms: 8.819171035 + 6.666666665 = 15.4858377
x = 15.4858377

Simplifying
x = 15.4858377


Subproblem 2
x + -6.666666665 = -8.819171035

Simplifying
x + -6.666666665 = -8.819171035

Reorder the terms:
-6.666666665 + x = -8.819171035

Solving
-6.666666665 + x = -8.819171035

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -8.819171035 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -8.819171035 + 6.666666665
x = -8.819171035 + 6.666666665

Combine like terms: -8.819171035 + 6.666666665 = -2.15250437
x = -2.15250437

Simplifying
x = -2.15250437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.4858377, -2.15250437}
Solution
x = {15.4858377, -2.15250437}

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