3x^2-188x-91010=0

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Solution for 3x^2-188x-91010=0 equation:


Simplifying
3x2 + -188x + -91010 = 0

Reorder the terms:
-91010 + -188x + 3x2 = 0

Solving
-91010 + -188x + 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'.
-30336.66667 + -62.66666667x + x2 = 0

Move the constant term to the right:

Add '30336.66667' to each side of the equation.
-30336.66667 + -62.66666667x + 30336.66667 + x2 = 0 + 30336.66667

Reorder the terms:
-30336.66667 + 30336.66667 + -62.66666667x + x2 = 0 + 30336.66667

Combine like terms: -30336.66667 + 30336.66667 = 0.00000
0.00000 + -62.66666667x + x2 = 0 + 30336.66667
-62.66666667x + x2 = 0 + 30336.66667

Combine like terms: 0 + 30336.66667 = 30336.66667
-62.66666667x + x2 = 30336.66667

The x term is -62.66666667x.  Take half its coefficient (-31.33333334).
Square it (981.7777782) and add it to both sides.

Add '981.7777782' to each side of the equation.
-62.66666667x + 981.7777782 + x2 = 30336.66667 + 981.7777782

Reorder the terms:
981.7777782 + -62.66666667x + x2 = 30336.66667 + 981.7777782

Combine like terms: 30336.66667 + 981.7777782 = 31318.4444482
981.7777782 + -62.66666667x + x2 = 31318.4444482

Factor a perfect square on the left side:
(x + -31.33333334)(x + -31.33333334) = 31318.4444482

Calculate the square root of the right side: 176.970179545

Break this problem into two subproblems by setting 
(x + -31.33333334) equal to 176.970179545 and -176.970179545.

Subproblem 1

x + -31.33333334 = 176.970179545 Simplifying x + -31.33333334 = 176.970179545 Reorder the terms: -31.33333334 + x = 176.970179545 Solving -31.33333334 + x = 176.970179545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.33333334' to each side of the equation. -31.33333334 + 31.33333334 + x = 176.970179545 + 31.33333334 Combine like terms: -31.33333334 + 31.33333334 = 0.00000000 0.00000000 + x = 176.970179545 + 31.33333334 x = 176.970179545 + 31.33333334 Combine like terms: 176.970179545 + 31.33333334 = 208.303512885 x = 208.303512885 Simplifying x = 208.303512885

Subproblem 2

x + -31.33333334 = -176.970179545 Simplifying x + -31.33333334 = -176.970179545 Reorder the terms: -31.33333334 + x = -176.970179545 Solving -31.33333334 + x = -176.970179545 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.33333334' to each side of the equation. -31.33333334 + 31.33333334 + x = -176.970179545 + 31.33333334 Combine like terms: -31.33333334 + 31.33333334 = 0.00000000 0.00000000 + x = -176.970179545 + 31.33333334 x = -176.970179545 + 31.33333334 Combine like terms: -176.970179545 + 31.33333334 = -145.636846205 x = -145.636846205 Simplifying x = -145.636846205

Solution

The solution to the problem is based on the solutions from the subproblems. x = {208.303512885, -145.636846205}

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