x^2+24.933x-305.4=0

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Solution for x^2+24.933x-305.4=0 equation: 


Simplifying
x2 + 24.933x + -305.4 = 0

Reorder the terms:
-305.4 + 24.933x + x2 = 0

Solving
-305.4 + 24.933x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '305.4' to each side of the equation.
-305.4 + 24.933x + 305.4 + x2 = 0 + 305.4

Reorder the terms:
-305.4 + 305.4 + 24.933x + x2 = 0 + 305.4

Combine like terms: -305.4 + 305.4 = 0.0
0.0 + 24.933x + x2 = 0 + 305.4
24.933x + x2 = 0 + 305.4

Combine like terms: 0 + 305.4 = 305.4
24.933x + x2 = 305.4

The x term is 24.933x.  Take half its coefficient (12.4665).
Square it (155.4136223) and add it to both sides.

Add '155.4136223' to each side of the equation.
24.933x + 155.4136223 + x2 = 305.4 + 155.4136223

Reorder the terms:
155.4136223 + 24.933x + x2 = 305.4 + 155.4136223

Combine like terms: 305.4 + 155.4136223 = 460.8136223
155.4136223 + 24.933x + x2 = 460.8136223

Factor a perfect square on the left side:
(x + 12.4665)(x + 12.4665) = 460.8136223

Calculate the square root of the right side: 21.466569877

Break this problem into two subproblems by setting 
(x + 12.4665) equal to 21.466569877 and -21.466569877.


Subproblem 1
x + 12.4665 = 21.466569877

Simplifying
x + 12.4665 = 21.466569877

Reorder the terms:
12.4665 + x = 21.466569877

Solving
12.4665 + x = 21.466569877

Solving for variable 'x'.

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

Add '-12.4665' to each side of the equation.
12.4665 + -12.4665 + x = 21.466569877 + -12.4665

Combine like terms: 12.4665 + -12.4665 = 0.0000
0.0000 + x = 21.466569877 + -12.4665
x = 21.466569877 + -12.4665

Combine like terms: 21.466569877 + -12.4665 = 9.000069877
x = 9.000069877

Simplifying
x = 9.000069877


Subproblem 2
x + 12.4665 = -21.466569877

Simplifying
x + 12.4665 = -21.466569877

Reorder the terms:
12.4665 + x = -21.466569877

Solving
12.4665 + x = -21.466569877

Solving for variable 'x'.

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

Add '-12.4665' to each side of the equation.
12.4665 + -12.4665 + x = -21.466569877 + -12.4665

Combine like terms: 12.4665 + -12.4665 = 0.0000
0.0000 + x = -21.466569877 + -12.4665
x = -21.466569877 + -12.4665

Combine like terms: -21.466569877 + -12.4665 = -33.933069877
x = -33.933069877

Simplifying
x = -33.933069877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.000069877, -33.933069877}

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