11x^2+6000x=-2500

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Solution for 11x^2+6000x=-2500 equation:


Simplifying
11x2 + 6000x = -2500

Reorder the terms:
6000x + 11x2 = -2500

Solving
6000x + 11x2 = -2500

Solving for variable 'x'.

Reorder the terms:
2500 + 6000x + 11x2 = -2500 + 2500

Combine like terms: -2500 + 2500 = 0
2500 + 6000x + 11x2 = 0

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

Divide each side by '11'.
227.2727273 + 545.4545455x + x2 = 0

Move the constant term to the right:

Add '-227.2727273' to each side of the equation.
227.2727273 + 545.4545455x + -227.2727273 + x2 = 0 + -227.2727273

Reorder the terms:
227.2727273 + -227.2727273 + 545.4545455x + x2 = 0 + -227.2727273

Combine like terms: 227.2727273 + -227.2727273 = 0.0000000
0.0000000 + 545.4545455x + x2 = 0 + -227.2727273
545.4545455x + x2 = 0 + -227.2727273

Combine like terms: 0 + -227.2727273 = -227.2727273
545.4545455x + x2 = -227.2727273

The x term is 545.4545455x.  Take half its coefficient (272.7272728).
Square it (74380.16533) and add it to both sides.

Add '74380.16533' to each side of the equation.
545.4545455x + 74380.16533 + x2 = -227.2727273 + 74380.16533

Reorder the terms:
74380.16533 + 545.4545455x + x2 = -227.2727273 + 74380.16533

Combine like terms: -227.2727273 + 74380.16533 = 74152.8926027
74380.16533 + 545.4545455x + x2 = 74152.8926027

Factor a perfect square on the left side:
(x + 272.7272728)(x + 272.7272728) = 74152.8926027

Calculate the square root of the right side: 272.310287361

Break this problem into two subproblems by setting 
(x + 272.7272728) equal to 272.310287361 and -272.310287361.

Subproblem 1

x + 272.7272728 = 272.310287361 Simplifying x + 272.7272728 = 272.310287361 Reorder the terms: 272.7272728 + x = 272.310287361 Solving 272.7272728 + x = 272.310287361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-272.7272728' to each side of the equation. 272.7272728 + -272.7272728 + x = 272.310287361 + -272.7272728 Combine like terms: 272.7272728 + -272.7272728 = 0.0000000 0.0000000 + x = 272.310287361 + -272.7272728 x = 272.310287361 + -272.7272728 Combine like terms: 272.310287361 + -272.7272728 = -0.416985439 x = -0.416985439 Simplifying x = -0.416985439

Subproblem 2

x + 272.7272728 = -272.310287361 Simplifying x + 272.7272728 = -272.310287361 Reorder the terms: 272.7272728 + x = -272.310287361 Solving 272.7272728 + x = -272.310287361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-272.7272728' to each side of the equation. 272.7272728 + -272.7272728 + x = -272.310287361 + -272.7272728 Combine like terms: 272.7272728 + -272.7272728 = 0.0000000 0.0000000 + x = -272.310287361 + -272.7272728 x = -272.310287361 + -272.7272728 Combine like terms: -272.310287361 + -272.7272728 = -545.037560161 x = -545.037560161 Simplifying x = -545.037560161

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.416985439, -545.037560161}

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