-350*x^2+2450*x+3099.53=0

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Solution for -350*x^2+2450*x+3099.53=0 equation: 


Simplifying
-350x2 + 2450x + 3099.53 = 0

Reorder the terms:
3099.53 + 2450x + -350x2 = 0

Solving
3099.53 + 2450x + -350x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-350 the coefficient of the squared term: 

Divide each side by '-350'.
-8.8558 + -7x + x2 = 0

Move the constant term to the right:

Add '8.8558' to each side of the equation.
-8.8558 + -7x + 8.8558 + x2 = 0 + 8.8558

Reorder the terms:
-8.8558 + 8.8558 + -7x + x2 = 0 + 8.8558

Combine like terms: -8.8558 + 8.8558 = 0.0000
0.0000 + -7x + x2 = 0 + 8.8558
-7x + x2 = 0 + 8.8558

Combine like terms: 0 + 8.8558 = 8.8558
-7x + x2 = 8.8558

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 8.8558 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 8.8558 + 12.25

Combine like terms: 8.8558 + 12.25 = 21.1058
12.25 + -7x + x2 = 21.1058

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 21.1058

Calculate the square root of the right side: 4.594104918

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.594104918 and -4.594104918.


Subproblem 1
x + -3.5 = 4.594104918

Simplifying
x + -3.5 = 4.594104918

Reorder the terms:
-3.5 + x = 4.594104918

Solving
-3.5 + x = 4.594104918

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.594104918 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.594104918 + 3.5
x = 4.594104918 + 3.5

Combine like terms: 4.594104918 + 3.5 = 8.094104918
x = 8.094104918

Simplifying
x = 8.094104918


Subproblem 2
x + -3.5 = -4.594104918

Simplifying
x + -3.5 = -4.594104918

Reorder the terms:
-3.5 + x = -4.594104918

Solving
-3.5 + x = -4.594104918

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.594104918 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.594104918 + 3.5
x = -4.594104918 + 3.5

Combine like terms: -4.594104918 + 3.5 = -1.094104918
x = -1.094104918

Simplifying
x = -1.094104918


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.094104918, -1.094104918}

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