3x^2+300x-2300=0

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Solution for 3x^2+300x-2300=0 equation:


Simplifying
3x2 + 300x + -2300 = 0

Reorder the terms:
-2300 + 300x + 3x2 = 0

Solving
-2300 + 300x + 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'.
-766.6666667 + 100x + x2 = 0

Move the constant term to the right:

Add '766.6666667' to each side of the equation.
-766.6666667 + 100x + 766.6666667 + x2 = 0 + 766.6666667

Reorder the terms:
-766.6666667 + 766.6666667 + 100x + x2 = 0 + 766.6666667

Combine like terms: -766.6666667 + 766.6666667 = 0.0000000
0.0000000 + 100x + x2 = 0 + 766.6666667
100x + x2 = 0 + 766.6666667

Combine like terms: 0 + 766.6666667 = 766.6666667
100x + x2 = 766.6666667

The x term is 100x.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x + 2500 + x2 = 766.6666667 + 2500

Reorder the terms:
2500 + 100x + x2 = 766.6666667 + 2500

Combine like terms: 766.6666667 + 2500 = 3266.6666667
2500 + 100x + x2 = 3266.6666667

Factor a perfect square on the left side:
(x + 50)(x + 50) = 3266.6666667

Calculate the square root of the right side: 57.154760665

Break this problem into two subproblems by setting 
(x + 50) equal to 57.154760665 and -57.154760665.

Subproblem 1

x + 50 = 57.154760665 Simplifying x + 50 = 57.154760665 Reorder the terms: 50 + x = 57.154760665 Solving 50 + x = 57.154760665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 57.154760665 + -50 Combine like terms: 50 + -50 = 0 0 + x = 57.154760665 + -50 x = 57.154760665 + -50 Combine like terms: 57.154760665 + -50 = 7.154760665 x = 7.154760665 Simplifying x = 7.154760665

Subproblem 2

x + 50 = -57.154760665 Simplifying x + 50 = -57.154760665 Reorder the terms: 50 + x = -57.154760665 Solving 50 + x = -57.154760665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -57.154760665 + -50 Combine like terms: 50 + -50 = 0 0 + x = -57.154760665 + -50 x = -57.154760665 + -50 Combine like terms: -57.154760665 + -50 = -107.154760665 x = -107.154760665 Simplifying x = -107.154760665

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.154760665, -107.154760665}

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