1000x^2+306x-714=0

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Solution for 1000x^2+306x-714=0 equation: 


Simplifying
1000x2 + 306x + -714 = 0

Reorder the terms:
-714 + 306x + 1000x2 = 0

Solving
-714 + 306x + 1000x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-357 + 153x + 500x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-357 + 153x + 500x2)' equal to zero and attempt to solve:

Simplifying
-357 + 153x + 500x2 = 0

Solving
-357 + 153x + 500x2 = 0

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

Divide each side by '500'.
-0.714 + 0.306x + x2 = 0.00

Move the constant term to the right:

Add '0.714' to each side of the equation.
-0.714 + 0.306x + 0.714 + x2 = 0.00 + 0.714

Reorder the terms:
-0.714 + 0.714 + 0.306x + x2 = 0.00 + 0.714

Combine like terms: -0.714 + 0.714 = 0.000
0.000 + 0.306x + x2 = 0.00 + 0.714
0.306x + x2 = 0.00 + 0.714

Combine like terms: 0.00 + 0.714 = 0.714
0.306x + x2 = 0.714

The x term is 0.306x.  Take half its coefficient (0.153).
Square it (0.023409) and add it to both sides.

Add '0.023409' to each side of the equation.
0.306x + 0.023409 + x2 = 0.714 + 0.023409

Reorder the terms:
0.023409 + 0.306x + x2 = 0.714 + 0.023409

Combine like terms: 0.714 + 0.023409 = 0.737409
0.023409 + 0.306x + x2 = 0.737409

Factor a perfect square on the left side:
(x + 0.153)(x + 0.153) = 0.737409

Calculate the square root of the right side: 0.858725218

Break this problem into two subproblems by setting 
(x + 0.153) equal to 0.858725218 and -0.858725218.


Subproblem 1
x + 0.153 = 0.858725218

Simplifying
x + 0.153 = 0.858725218

Reorder the terms:
0.153 + x = 0.858725218

Solving
0.153 + x = 0.858725218

Solving for variable 'x'.

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

Add '-0.153' to each side of the equation.
0.153 + -0.153 + x = 0.858725218 + -0.153

Combine like terms: 0.153 + -0.153 = 0.000
0.000 + x = 0.858725218 + -0.153
x = 0.858725218 + -0.153

Combine like terms: 0.858725218 + -0.153 = 0.705725218
x = 0.705725218

Simplifying
x = 0.705725218


Subproblem 2
x + 0.153 = -0.858725218

Simplifying
x + 0.153 = -0.858725218

Reorder the terms:
0.153 + x = -0.858725218

Solving
0.153 + x = -0.858725218

Solving for variable 'x'.

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

Add '-0.153' to each side of the equation.
0.153 + -0.153 + x = -0.858725218 + -0.153

Combine like terms: 0.153 + -0.153 = 0.000
0.000 + x = -0.858725218 + -0.153
x = -0.858725218 + -0.153

Combine like terms: -0.858725218 + -0.153 = -1.011725218
x = -1.011725218

Simplifying
x = -1.011725218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.705725218, -1.011725218}
Solution
x = {0.705725218, -1.011725218}

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