-37x^2+888x-2289=0

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Solution for -37x^2+888x-2289=0 equation: 


Simplifying
-37x2 + 888x + -2289 = 0

Reorder the terms:
-2289 + 888x + -37x2 = 0

Solving
-2289 + 888x + -37x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-37 the coefficient of the squared term: 

Divide each side by '-37'.
61.86486486 + -24x + x2 = 0

Move the constant term to the right:

Add '-61.86486486' to each side of the equation.
61.86486486 + -24x + -61.86486486 + x2 = 0 + -61.86486486

Reorder the terms:
61.86486486 + -61.86486486 + -24x + x2 = 0 + -61.86486486

Combine like terms: 61.86486486 + -61.86486486 = 0.00000000
0.00000000 + -24x + x2 = 0 + -61.86486486
-24x + x2 = 0 + -61.86486486

Combine like terms: 0 + -61.86486486 = -61.86486486
-24x + x2 = -61.86486486

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -61.86486486 + 144

Reorder the terms:
144 + -24x + x2 = -61.86486486 + 144

Combine like terms: -61.86486486 + 144 = 82.13513514
144 + -24x + x2 = 82.13513514

Factor a perfect square on the left side:
(x + -12)(x + -12) = 82.13513514

Calculate the square root of the right side: 9.062843656

Break this problem into two subproblems by setting 
(x + -12) equal to 9.062843656 and -9.062843656.


Subproblem 1
x + -12 = 9.062843656

Simplifying
x + -12 = 9.062843656

Reorder the terms:
-12 + x = 9.062843656

Solving
-12 + x = 9.062843656

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 9.062843656 + 12

Combine like terms: -12 + 12 = 0
0 + x = 9.062843656 + 12
x = 9.062843656 + 12

Combine like terms: 9.062843656 + 12 = 21.062843656
x = 21.062843656

Simplifying
x = 21.062843656


Subproblem 2
x + -12 = -9.062843656

Simplifying
x + -12 = -9.062843656

Reorder the terms:
-12 + x = -9.062843656

Solving
-12 + x = -9.062843656

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -9.062843656 + 12

Combine like terms: -12 + 12 = 0
0 + x = -9.062843656 + 12
x = -9.062843656 + 12

Combine like terms: -9.062843656 + 12 = 2.937156344
x = 2.937156344

Simplifying
x = 2.937156344


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.062843656, 2.937156344}

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