1000x^2+1300x-2570=0

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Solution for 1000x^2+1300x-2570=0 equation: 


Simplifying
1000x2 + 1300x + -2570 = 0

Reorder the terms:
-2570 + 1300x + 1000x2 = 0

Solving
-2570 + 1300x + 1000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-257 + 130x + 100x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-257 + 130x + 100x2)' equal to zero and attempt to solve:

Simplifying
-257 + 130x + 100x2 = 0

Solving
-257 + 130x + 100x2 = 0

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

Divide each side by '100'.
-2.57 + 1.3x + x2 = 0.00

Move the constant term to the right:

Add '2.57' to each side of the equation.
-2.57 + 1.3x + 2.57 + x2 = 0.00 + 2.57

Reorder the terms:
-2.57 + 2.57 + 1.3x + x2 = 0.00 + 2.57

Combine like terms: -2.57 + 2.57 = 0.00
0.00 + 1.3x + x2 = 0.00 + 2.57
1.3x + x2 = 0.00 + 2.57

Combine like terms: 0.00 + 2.57 = 2.57
1.3x + x2 = 2.57

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 2.57 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 2.57 + 0.4225

Combine like terms: 2.57 + 0.4225 = 2.9925
0.4225 + 1.3x + x2 = 2.9925

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 2.9925

Calculate the square root of the right side: 1.729884389

Break this problem into two subproblems by setting 
(x + 0.65) equal to 1.729884389 and -1.729884389.


Subproblem 1
x + 0.65 = 1.729884389

Simplifying
x + 0.65 = 1.729884389

Reorder the terms:
0.65 + x = 1.729884389

Solving
0.65 + x = 1.729884389

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 1.729884389 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 1.729884389 + -0.65
x = 1.729884389 + -0.65

Combine like terms: 1.729884389 + -0.65 = 1.079884389
x = 1.079884389

Simplifying
x = 1.079884389


Subproblem 2
x + 0.65 = -1.729884389

Simplifying
x + 0.65 = -1.729884389

Reorder the terms:
0.65 + x = -1.729884389

Solving
0.65 + x = -1.729884389

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -1.729884389 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -1.729884389 + -0.65
x = -1.729884389 + -0.65

Combine like terms: -1.729884389 + -0.65 = -2.379884389
x = -2.379884389

Simplifying
x = -2.379884389


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.079884389, -2.379884389}
Solution
x = {1.079884389, -2.379884389}

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