4418.75-3514.64651450637x+-4805.66085751061x^2=0

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Solution for 4418.75-3514.64651450637x+-4805.66085751061x^2=0 equation:


Simplifying
4418.75 + -3514.64651450637x + -4805.66085751061x2 = 0

Solving
4418.75 + -3514.64651450637x + -4805.66085751061x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4805.66085751061 the coefficient of the squared term: 

Divide each side by '-4805.66085751061'.
-0.9194885222 + 0.7313555032x + x2 = 0

Move the constant term to the right:

Add '0.9194885222' to each side of the equation.
-0.9194885222 + 0.7313555032x + 0.9194885222 + x2 = 0 + 0.9194885222

Reorder the terms:
-0.9194885222 + 0.9194885222 + 0.7313555032x + x2 = 0 + 0.9194885222

Combine like terms: -0.9194885222 + 0.9194885222 = 0.0000000000
0.0000000000 + 0.7313555032x + x2 = 0 + 0.9194885222
0.7313555032x + x2 = 0 + 0.9194885222

Combine like terms: 0 + 0.9194885222 = 0.9194885222
0.7313555032x + x2 = 0.9194885222

The x term is 0.7313555032x.  Take half its coefficient (0.3656777516).
Square it (0.1337202180) and add it to both sides.

Add '0.1337202180' to each side of the equation.
0.7313555032x + 0.1337202180 + x2 = 0.9194885222 + 0.1337202180

Reorder the terms:
0.1337202180 + 0.7313555032x + x2 = 0.9194885222 + 0.1337202180

Combine like terms: 0.9194885222 + 0.1337202180 = 1.0532087402
0.1337202180 + 0.7313555032x + x2 = 1.0532087402

Factor a perfect square on the left side:
(x + 0.3656777516)(x + 0.3656777516) = 1.0532087402

Calculate the square root of the right side: 1.026259587

Break this problem into two subproblems by setting 
(x + 0.3656777516) equal to 1.026259587 and -1.026259587.

Subproblem 1

x + 0.3656777516 = 1.026259587 Simplifying x + 0.3656777516 = 1.026259587 Reorder the terms: 0.3656777516 + x = 1.026259587 Solving 0.3656777516 + x = 1.026259587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3656777516' to each side of the equation. 0.3656777516 + -0.3656777516 + x = 1.026259587 + -0.3656777516 Combine like terms: 0.3656777516 + -0.3656777516 = 0.0000000000 0.0000000000 + x = 1.026259587 + -0.3656777516 x = 1.026259587 + -0.3656777516 Combine like terms: 1.026259587 + -0.3656777516 = 0.6605818354 x = 0.6605818354 Simplifying x = 0.6605818354

Subproblem 2

x + 0.3656777516 = -1.026259587 Simplifying x + 0.3656777516 = -1.026259587 Reorder the terms: 0.3656777516 + x = -1.026259587 Solving 0.3656777516 + x = -1.026259587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3656777516' to each side of the equation. 0.3656777516 + -0.3656777516 + x = -1.026259587 + -0.3656777516 Combine like terms: 0.3656777516 + -0.3656777516 = 0.0000000000 0.0000000000 + x = -1.026259587 + -0.3656777516 x = -1.026259587 + -0.3656777516 Combine like terms: -1.026259587 + -0.3656777516 = -1.3919373386 x = -1.3919373386 Simplifying x = -1.3919373386

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6605818354, -1.3919373386}

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