10x^2+400x-2304=0

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Solution for 10x^2+400x-2304=0 equation: 


Simplifying
10x2 + 400x + -2304 = 0

Reorder the terms:
-2304 + 400x + 10x2 = 0

Solving
-2304 + 400x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1152 + 200x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1152 + 200x + 5x2)' equal to zero and attempt to solve:

Simplifying
-1152 + 200x + 5x2 = 0

Solving
-1152 + 200x + 5x2 = 0

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

Divide each side by '5'.
-230.4 + 40x + x2 = 0

Move the constant term to the right:

Add '230.4' to each side of the equation.
-230.4 + 40x + 230.4 + x2 = 0 + 230.4

Reorder the terms:
-230.4 + 230.4 + 40x + x2 = 0 + 230.4

Combine like terms: -230.4 + 230.4 = 0.0
0.0 + 40x + x2 = 0 + 230.4
40x + x2 = 0 + 230.4

Combine like terms: 0 + 230.4 = 230.4
40x + x2 = 230.4

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 230.4 + 400

Reorder the terms:
400 + 40x + x2 = 230.4 + 400

Combine like terms: 230.4 + 400 = 630.4
400 + 40x + x2 = 630.4

Factor a perfect square on the left side:
(x + 20)(x + 20) = 630.4

Calculate the square root of the right side: 25.107767722

Break this problem into two subproblems by setting 
(x + 20) equal to 25.107767722 and -25.107767722.


Subproblem 1
x + 20 = 25.107767722

Simplifying
x + 20 = 25.107767722

Reorder the terms:
20 + x = 25.107767722

Solving
20 + x = 25.107767722

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = 25.107767722 + -20

Combine like terms: 20 + -20 = 0
0 + x = 25.107767722 + -20
x = 25.107767722 + -20

Combine like terms: 25.107767722 + -20 = 5.107767722
x = 5.107767722

Simplifying
x = 5.107767722


Subproblem 2
x + 20 = -25.107767722

Simplifying
x + 20 = -25.107767722

Reorder the terms:
20 + x = -25.107767722

Solving
20 + x = -25.107767722

Solving for variable 'x'.

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

Add '-20' to each side of the equation.
20 + -20 + x = -25.107767722 + -20

Combine like terms: 20 + -20 = 0
0 + x = -25.107767722 + -20
x = -25.107767722 + -20

Combine like terms: -25.107767722 + -20 = -45.107767722
x = -45.107767722

Simplifying
x = -45.107767722


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.107767722, -45.107767722}
Solution
x = {5.107767722, -45.107767722}

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