10x^2-300x-1250=0

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Solution for 10x^2-300x-1250=0 equation: 


Simplifying
10x2 + -300x + -1250 = 0

Reorder the terms:
-1250 + -300x + 10x2 = 0

Solving
-1250 + -300x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-125 + -30x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-125 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
-125 + -30x + x2 = 0

Solving
-125 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -30x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + -30x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -30x + x2 = 0 + 125
-30x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
-30x + x2 = 125

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 125 + 225

Reorder the terms:
225 + -30x + x2 = 125 + 225

Combine like terms: 125 + 225 = 350
225 + -30x + x2 = 350

Factor a perfect square on the left side:
(x + -15)(x + -15) = 350

Calculate the square root of the right side: 18.708286934

Break this problem into two subproblems by setting 
(x + -15) equal to 18.708286934 and -18.708286934.


Subproblem 1
x + -15 = 18.708286934

Simplifying
x + -15 = 18.708286934

Reorder the terms:
-15 + x = 18.708286934

Solving
-15 + x = 18.708286934

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 18.708286934 + 15

Combine like terms: -15 + 15 = 0
0 + x = 18.708286934 + 15
x = 18.708286934 + 15

Combine like terms: 18.708286934 + 15 = 33.708286934
x = 33.708286934

Simplifying
x = 33.708286934


Subproblem 2
x + -15 = -18.708286934

Simplifying
x + -15 = -18.708286934

Reorder the terms:
-15 + x = -18.708286934

Solving
-15 + x = -18.708286934

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -18.708286934 + 15

Combine like terms: -15 + 15 = 0
0 + x = -18.708286934 + 15
x = -18.708286934 + 15

Combine like terms: -18.708286934 + 15 = -3.708286934
x = -3.708286934

Simplifying
x = -3.708286934


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.708286934, -3.708286934}
Solution
x = {33.708286934, -3.708286934}

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