-10x^2+335x+3700=0

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Solution for -10x^2+335x+3700=0 equation: 


Simplifying
-10x2 + 335x + 3700 = 0

Reorder the terms:
3700 + 335x + -10x2 = 0

Solving
3700 + 335x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(740 + 67x + -2x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(740 + 67x + -2x2)' equal to zero and attempt to solve:

Simplifying
740 + 67x + -2x2 = 0

Solving
740 + 67x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-370 + -33.5x + x2 = 0

Move the constant term to the right:

Add '370' to each side of the equation.
-370 + -33.5x + 370 + x2 = 0 + 370

Reorder the terms:
-370 + 370 + -33.5x + x2 = 0 + 370

Combine like terms: -370 + 370 = 0
0 + -33.5x + x2 = 0 + 370
-33.5x + x2 = 0 + 370

Combine like terms: 0 + 370 = 370
-33.5x + x2 = 370

The x term is -33.5x.  Take half its coefficient (-16.75).
Square it (280.5625) and add it to both sides.

Add '280.5625' to each side of the equation.
-33.5x + 280.5625 + x2 = 370 + 280.5625

Reorder the terms:
280.5625 + -33.5x + x2 = 370 + 280.5625

Combine like terms: 370 + 280.5625 = 650.5625
280.5625 + -33.5x + x2 = 650.5625

Factor a perfect square on the left side:
(x + -16.75)(x + -16.75) = 650.5625

Calculate the square root of the right side: 25.506126715

Break this problem into two subproblems by setting 
(x + -16.75) equal to 25.506126715 and -25.506126715.


Subproblem 1
x + -16.75 = 25.506126715

Simplifying
x + -16.75 = 25.506126715

Reorder the terms:
-16.75 + x = 25.506126715

Solving
-16.75 + x = 25.506126715

Solving for variable 'x'.

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

Add '16.75' to each side of the equation.
-16.75 + 16.75 + x = 25.506126715 + 16.75

Combine like terms: -16.75 + 16.75 = 0.00
0.00 + x = 25.506126715 + 16.75
x = 25.506126715 + 16.75

Combine like terms: 25.506126715 + 16.75 = 42.256126715
x = 42.256126715

Simplifying
x = 42.256126715


Subproblem 2
x + -16.75 = -25.506126715

Simplifying
x + -16.75 = -25.506126715

Reorder the terms:
-16.75 + x = -25.506126715

Solving
-16.75 + x = -25.506126715

Solving for variable 'x'.

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

Add '16.75' to each side of the equation.
-16.75 + 16.75 + x = -25.506126715 + 16.75

Combine like terms: -16.75 + 16.75 = 0.00
0.00 + x = -25.506126715 + 16.75
x = -25.506126715 + 16.75

Combine like terms: -25.506126715 + 16.75 = -8.756126715
x = -8.756126715

Simplifying
x = -8.756126715


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.256126715, -8.756126715}
Solution
x = {42.256126715, -8.756126715}

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