2x^2+380x+8400=1500

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Solution for 2x^2+380x+8400=1500 equation: 


Simplifying
2x2 + 380x + 8400 = 1500

Reorder the terms:
8400 + 380x + 2x2 = 1500

Solving
8400 + 380x + 2x2 = 1500

Solving for variable 'x'.

Reorder the terms:
8400 + -1500 + 380x + 2x2 = 1500 + -1500

Combine like terms: 8400 + -1500 = 6900
6900 + 380x + 2x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
6900 + 380x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3450 + 190x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3450 + 190x + x2)' equal to zero and attempt to solve:

Simplifying
3450 + 190x + x2 = 0

Solving
3450 + 190x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3450' to each side of the equation.
3450 + 190x + -3450 + x2 = 0 + -3450

Reorder the terms:
3450 + -3450 + 190x + x2 = 0 + -3450

Combine like terms: 3450 + -3450 = 0
0 + 190x + x2 = 0 + -3450
190x + x2 = 0 + -3450

Combine like terms: 0 + -3450 = -3450
190x + x2 = -3450

The x term is 190x.  Take half its coefficient (95).
Square it (9025) and add it to both sides.

Add '9025' to each side of the equation.
190x + 9025 + x2 = -3450 + 9025

Reorder the terms:
9025 + 190x + x2 = -3450 + 9025

Combine like terms: -3450 + 9025 = 5575
9025 + 190x + x2 = 5575

Factor a perfect square on the left side:
(x + 95)(x + 95) = 5575

Calculate the square root of the right side: 74.665922615

Break this problem into two subproblems by setting 
(x + 95) equal to 74.665922615 and -74.665922615.


Subproblem 1
x + 95 = 74.665922615

Simplifying
x + 95 = 74.665922615

Reorder the terms:
95 + x = 74.665922615

Solving
95 + x = 74.665922615

Solving for variable 'x'.

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

Add '-95' to each side of the equation.
95 + -95 + x = 74.665922615 + -95

Combine like terms: 95 + -95 = 0
0 + x = 74.665922615 + -95
x = 74.665922615 + -95

Combine like terms: 74.665922615 + -95 = -20.334077385
x = -20.334077385

Simplifying
x = -20.334077385


Subproblem 2
x + 95 = -74.665922615

Simplifying
x + 95 = -74.665922615

Reorder the terms:
95 + x = -74.665922615

Solving
95 + x = -74.665922615

Solving for variable 'x'.

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

Add '-95' to each side of the equation.
95 + -95 + x = -74.665922615 + -95

Combine like terms: 95 + -95 = 0
0 + x = -74.665922615 + -95
x = -74.665922615 + -95

Combine like terms: -74.665922615 + -95 = -169.665922615
x = -169.665922615

Simplifying
x = -169.665922615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-20.334077385, -169.665922615}
Solution
x = {-20.334077385, -169.665922615}

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