3x^2+7x-10000=0

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Solution for 3x^2+7x-10000=0 equation: 


Simplifying
3x2 + 7x + -10000 = 0

Reorder the terms:
-10000 + 7x + 3x2 = 0

Solving
-10000 + 7x + 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'.
-3333.333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '3333.333333' to each side of the equation.
-3333.333333 + 2.333333333x + 3333.333333 + x2 = 0 + 3333.333333

Reorder the terms:
-3333.333333 + 3333.333333 + 2.333333333x + x2 = 0 + 3333.333333

Combine like terms: -3333.333333 + 3333.333333 = 0.000000
0.000000 + 2.333333333x + x2 = 0 + 3333.333333
2.333333333x + x2 = 0 + 3333.333333

Combine like terms: 0 + 3333.333333 = 3333.333333
2.333333333x + x2 = 3333.333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 3333.333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 3333.333333 + 1.361111112

Combine like terms: 3333.333333 + 1.361111112 = 3334.694444112
1.361111112 + 2.333333333x + x2 = 3334.694444112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 3334.694444112

Calculate the square root of the right side: 57.746813281

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 57.746813281 and -57.746813281.


Subproblem 1
x + 1.166666667 = 57.746813281

Simplifying
x + 1.166666667 = 57.746813281

Reorder the terms:
1.166666667 + x = 57.746813281

Solving
1.166666667 + x = 57.746813281

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 57.746813281 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 57.746813281 + -1.166666667
x = 57.746813281 + -1.166666667

Combine like terms: 57.746813281 + -1.166666667 = 56.580146614
x = 56.580146614

Simplifying
x = 56.580146614


Subproblem 2
x + 1.166666667 = -57.746813281

Simplifying
x + 1.166666667 = -57.746813281

Reorder the terms:
1.166666667 + x = -57.746813281

Solving
1.166666667 + x = -57.746813281

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -57.746813281 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -57.746813281 + -1.166666667
x = -57.746813281 + -1.166666667

Combine like terms: -57.746813281 + -1.166666667 = -58.913479948
x = -58.913479948

Simplifying
x = -58.913479948


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.580146614, -58.913479948}

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