-100x^2+2410x+22500=0

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Solution for -100x^2+2410x+22500=0 equation: 


Simplifying
-100x2 + 2410x + 22500 = 0

Reorder the terms:
22500 + 2410x + -100x2 = 0

Solving
22500 + 2410x + -100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(2250 + 241x + -10x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(2250 + 241x + -10x2)' equal to zero and attempt to solve:

Simplifying
2250 + 241x + -10x2 = 0

Solving
2250 + 241x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-225 + -24.1x + x2 = 0.0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -24.1x + 225 + x2 = 0.0 + 225

Reorder the terms:
-225 + 225 + -24.1x + x2 = 0.0 + 225

Combine like terms: -225 + 225 = 0
0 + -24.1x + x2 = 0.0 + 225
-24.1x + x2 = 0.0 + 225

Combine like terms: 0.0 + 225 = 225
-24.1x + x2 = 225

The x term is -24.1x.  Take half its coefficient (-12.05).
Square it (145.2025) and add it to both sides.

Add '145.2025' to each side of the equation.
-24.1x + 145.2025 + x2 = 225 + 145.2025

Reorder the terms:
145.2025 + -24.1x + x2 = 225 + 145.2025

Combine like terms: 225 + 145.2025 = 370.2025
145.2025 + -24.1x + x2 = 370.2025

Factor a perfect square on the left side:
(x + -12.05)(x + -12.05) = 370.2025

Calculate the square root of the right side: 19.240647079

Break this problem into two subproblems by setting 
(x + -12.05) equal to 19.240647079 and -19.240647079.


Subproblem 1
x + -12.05 = 19.240647079

Simplifying
x + -12.05 = 19.240647079

Reorder the terms:
-12.05 + x = 19.240647079

Solving
-12.05 + x = 19.240647079

Solving for variable 'x'.

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

Add '12.05' to each side of the equation.
-12.05 + 12.05 + x = 19.240647079 + 12.05

Combine like terms: -12.05 + 12.05 = 0.00
0.00 + x = 19.240647079 + 12.05
x = 19.240647079 + 12.05

Combine like terms: 19.240647079 + 12.05 = 31.290647079
x = 31.290647079

Simplifying
x = 31.290647079


Subproblem 2
x + -12.05 = -19.240647079

Simplifying
x + -12.05 = -19.240647079

Reorder the terms:
-12.05 + x = -19.240647079

Solving
-12.05 + x = -19.240647079

Solving for variable 'x'.

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

Add '12.05' to each side of the equation.
-12.05 + 12.05 + x = -19.240647079 + 12.05

Combine like terms: -12.05 + 12.05 = 0.00
0.00 + x = -19.240647079 + 12.05
x = -19.240647079 + 12.05

Combine like terms: -19.240647079 + 12.05 = -7.190647079
x = -7.190647079

Simplifying
x = -7.190647079


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.290647079, -7.190647079}
Solution
x = {31.290647079, -7.190647079}

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