449174=0.6213x^2+468.84x+14091

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Solution for 449174=0.6213x^2+468.84x+14091 equation:


Simplifying
449174 = 0.6213x2 + 468.84x + 14091

Reorder the terms:
449174 = 14091 + 468.84x + 0.6213x2

Solving
449174 = 14091 + 468.84x + 0.6213x2

Solving for variable 'x'.

Combine like terms: 449174 + -14091 = 435083
435083 + -468.84x + -0.6213x2 = 14091 + 468.84x + 0.6213x2 + -14091 + -468.84x + -0.6213x2

Reorder the terms:
435083 + -468.84x + -0.6213x2 = 14091 + -14091 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2

Combine like terms: 14091 + -14091 = 0
435083 + -468.84x + -0.6213x2 = 0 + 468.84x + -468.84x + 0.6213x2 + -0.6213x2
435083 + -468.84x + -0.6213x2 = 468.84x + -468.84x + 0.6213x2 + -0.6213x2

Combine like terms: 468.84x + -468.84x = 0.00
435083 + -468.84x + -0.6213x2 = 0.00 + 0.6213x2 + -0.6213x2
435083 + -468.84x + -0.6213x2 = 0.6213x2 + -0.6213x2

Combine like terms: 0.6213x2 + -0.6213x2 = 0.0000
435083 + -468.84x + -0.6213x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.6213 the coefficient of the squared term: 

Divide each side by '-0.6213'.
-700278.4484 + 754.6112989x + x2 = 0

Move the constant term to the right:

Add '700278.4484' to each side of the equation.
-700278.4484 + 754.6112989x + 700278.4484 + x2 = 0 + 700278.4484

Reorder the terms:
-700278.4484 + 700278.4484 + 754.6112989x + x2 = 0 + 700278.4484

Combine like terms: -700278.4484 + 700278.4484 = 0.0000
0.0000 + 754.6112989x + x2 = 0 + 700278.4484
754.6112989x + x2 = 0 + 700278.4484

Combine like terms: 0 + 700278.4484 = 700278.4484
754.6112989x + x2 = 700278.4484

The x term is 754.6112989x.  Take half its coefficient (377.3056495).
Square it (142359.5531) and add it to both sides.

Add '142359.5531' to each side of the equation.
754.6112989x + 142359.5531 + x2 = 700278.4484 + 142359.5531

Reorder the terms:
142359.5531 + 754.6112989x + x2 = 700278.4484 + 142359.5531

Combine like terms: 700278.4484 + 142359.5531 = 842638.0015
142359.5531 + 754.6112989x + x2 = 842638.0015

Factor a perfect square on the left side:
(x + 377.3056495)(x + 377.3056495) = 842638.0015

Calculate the square root of the right side: 917.953158663

Break this problem into two subproblems by setting 
(x + 377.3056495) equal to 917.953158663 and -917.953158663.

Subproblem 1

x + 377.3056495 = 917.953158663 Simplifying x + 377.3056495 = 917.953158663 Reorder the terms: 377.3056495 + x = 917.953158663 Solving 377.3056495 + x = 917.953158663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = 917.953158663 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = 917.953158663 + -377.3056495 x = 917.953158663 + -377.3056495 Combine like terms: 917.953158663 + -377.3056495 = 540.647509163 x = 540.647509163 Simplifying x = 540.647509163

Subproblem 2

x + 377.3056495 = -917.953158663 Simplifying x + 377.3056495 = -917.953158663 Reorder the terms: 377.3056495 + x = -917.953158663 Solving 377.3056495 + x = -917.953158663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-377.3056495' to each side of the equation. 377.3056495 + -377.3056495 + x = -917.953158663 + -377.3056495 Combine like terms: 377.3056495 + -377.3056495 = 0.0000000 0.0000000 + x = -917.953158663 + -377.3056495 x = -917.953158663 + -377.3056495 Combine like terms: -917.953158663 + -377.3056495 = -1295.258808163 x = -1295.258808163 Simplifying x = -1295.258808163

Solution

The solution to the problem is based on the solutions from the subproblems. x = {540.647509163, -1295.258808163}

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