250x^2+310x-600=0

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Solution for 250x^2+310x-600=0 equation: 


Simplifying
250x2 + 310x + -600 = 0

Reorder the terms:
-600 + 310x + 250x2 = 0

Solving
-600 + 310x + 250x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-60 + 31x + 25x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-60 + 31x + 25x2)' equal to zero and attempt to solve:

Simplifying
-60 + 31x + 25x2 = 0

Solving
-60 + 31x + 25x2 = 0

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

Divide each side by '25'.
-2.4 + 1.24x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 1.24x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 1.24x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 1.24x + x2 = 0 + 2.4
1.24x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
1.24x + x2 = 2.4

The x term is 1.24x.  Take half its coefficient (0.62).
Square it (0.3844) and add it to both sides.

Add '0.3844' to each side of the equation.
1.24x + 0.3844 + x2 = 2.4 + 0.3844

Reorder the terms:
0.3844 + 1.24x + x2 = 2.4 + 0.3844

Combine like terms: 2.4 + 0.3844 = 2.7844
0.3844 + 1.24x + x2 = 2.7844

Factor a perfect square on the left side:
(x + 0.62)(x + 0.62) = 2.7844

Calculate the square root of the right side: 1.668652151

Break this problem into two subproblems by setting 
(x + 0.62) equal to 1.668652151 and -1.668652151.


Subproblem 1
x + 0.62 = 1.668652151

Simplifying
x + 0.62 = 1.668652151

Reorder the terms:
0.62 + x = 1.668652151

Solving
0.62 + x = 1.668652151

Solving for variable 'x'.

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

Add '-0.62' to each side of the equation.
0.62 + -0.62 + x = 1.668652151 + -0.62

Combine like terms: 0.62 + -0.62 = 0.00
0.00 + x = 1.668652151 + -0.62
x = 1.668652151 + -0.62

Combine like terms: 1.668652151 + -0.62 = 1.048652151
x = 1.048652151

Simplifying
x = 1.048652151


Subproblem 2
x + 0.62 = -1.668652151

Simplifying
x + 0.62 = -1.668652151

Reorder the terms:
0.62 + x = -1.668652151

Solving
0.62 + x = -1.668652151

Solving for variable 'x'.

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

Add '-0.62' to each side of the equation.
0.62 + -0.62 + x = -1.668652151 + -0.62

Combine like terms: 0.62 + -0.62 = 0.00
0.00 + x = -1.668652151 + -0.62
x = -1.668652151 + -0.62

Combine like terms: -1.668652151 + -0.62 = -2.288652151
x = -2.288652151

Simplifying
x = -2.288652151


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.048652151, -2.288652151}
Solution
x = {1.048652151, -2.288652151}

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