-1x^2+314.019418x+24673.20799626468=0

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Solution for -1x^2+314.019418x+24673.20799626468=0 equation: 


Simplifying
-1x2 + 314.019418x + 24673.20799626468 = 0

Reorder the terms:
24673.20799626468 + 314.019418x + -1x2 = 0

Solving
24673.20799626468 + 314.019418x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-24673.208 + -314.019418x + x2 = 0

Move the constant term to the right:

Add '24673.208' to each side of the equation.
-24673.208 + -314.019418x + 24673.208 + x2 = 0 + 24673.208

Reorder the terms:
-24673.208 + 24673.208 + -314.019418x + x2 = 0 + 24673.208

Combine like terms: -24673.208 + 24673.208 = 0.000
0.000 + -314.019418x + x2 = 0 + 24673.208
-314.019418x + x2 = 0 + 24673.208

Combine like terms: 0 + 24673.208 = 24673.208
-314.019418x + x2 = 24673.208

The x term is -314.019418x.  Take half its coefficient (-157.009709).
Square it (24652.04872) and add it to both sides.

Add '24652.04872' to each side of the equation.
-314.019418x + 24652.04872 + x2 = 24673.208 + 24652.04872

Reorder the terms:
24652.04872 + -314.019418x + x2 = 24673.208 + 24652.04872

Combine like terms: 24673.208 + 24652.04872 = 49325.25672
24652.04872 + -314.019418x + x2 = 49325.25672

Factor a perfect square on the left side:
(x + -157.009709)(x + -157.009709) = 49325.25672

Calculate the square root of the right side: 222.092901102

Break this problem into two subproblems by setting 
(x + -157.009709) equal to 222.092901102 and -222.092901102.


Subproblem 1
x + -157.009709 = 222.092901102

Simplifying
x + -157.009709 = 222.092901102

Reorder the terms:
-157.009709 + x = 222.092901102

Solving
-157.009709 + x = 222.092901102

Solving for variable 'x'.

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

Add '157.009709' to each side of the equation.
-157.009709 + 157.009709 + x = 222.092901102 + 157.009709

Combine like terms: -157.009709 + 157.009709 = 0.000000
0.000000 + x = 222.092901102 + 157.009709
x = 222.092901102 + 157.009709

Combine like terms: 222.092901102 + 157.009709 = 379.102610102
x = 379.102610102

Simplifying
x = 379.102610102


Subproblem 2
x + -157.009709 = -222.092901102

Simplifying
x + -157.009709 = -222.092901102

Reorder the terms:
-157.009709 + x = -222.092901102

Solving
-157.009709 + x = -222.092901102

Solving for variable 'x'.

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

Add '157.009709' to each side of the equation.
-157.009709 + 157.009709 + x = -222.092901102 + 157.009709

Combine like terms: -157.009709 + 157.009709 = 0.000000
0.000000 + x = -222.092901102 + 157.009709
x = -222.092901102 + 157.009709

Combine like terms: -222.092901102 + 157.009709 = -65.083192102
x = -65.083192102

Simplifying
x = -65.083192102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {379.102610102, -65.083192102}

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