x^2+1.84x-12.25=0

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Solution for x^2+1.84x-12.25=0 equation: 


Simplifying
x2 + 1.84x + -12.25 = 0

Reorder the terms:
-12.25 + 1.84x + x2 = 0

Solving
-12.25 + 1.84x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 1.84x + 12.25 + x2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 1.84x + x2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 1.84x + x2 = 0 + 12.25
1.84x + x2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
1.84x + x2 = 12.25

The x term is 1.84x.  Take half its coefficient (0.92).
Square it (0.8464) and add it to both sides.

Add '0.8464' to each side of the equation.
1.84x + 0.8464 + x2 = 12.25 + 0.8464

Reorder the terms:
0.8464 + 1.84x + x2 = 12.25 + 0.8464

Combine like terms: 12.25 + 0.8464 = 13.0964
0.8464 + 1.84x + x2 = 13.0964

Factor a perfect square on the left side:
(x + 0.92)(x + 0.92) = 13.0964

Calculate the square root of the right side: 3.618894859

Break this problem into two subproblems by setting 
(x + 0.92) equal to 3.618894859 and -3.618894859.


Subproblem 1
x + 0.92 = 3.618894859

Simplifying
x + 0.92 = 3.618894859

Reorder the terms:
0.92 + x = 3.618894859

Solving
0.92 + x = 3.618894859

Solving for variable 'x'.

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

Add '-0.92' to each side of the equation.
0.92 + -0.92 + x = 3.618894859 + -0.92

Combine like terms: 0.92 + -0.92 = 0.00
0.00 + x = 3.618894859 + -0.92
x = 3.618894859 + -0.92

Combine like terms: 3.618894859 + -0.92 = 2.698894859
x = 2.698894859

Simplifying
x = 2.698894859


Subproblem 2
x + 0.92 = -3.618894859

Simplifying
x + 0.92 = -3.618894859

Reorder the terms:
0.92 + x = -3.618894859

Solving
0.92 + x = -3.618894859

Solving for variable 'x'.

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

Add '-0.92' to each side of the equation.
0.92 + -0.92 + x = -3.618894859 + -0.92

Combine like terms: 0.92 + -0.92 = 0.00
0.00 + x = -3.618894859 + -0.92
x = -3.618894859 + -0.92

Combine like terms: -3.618894859 + -0.92 = -4.538894859
x = -4.538894859

Simplifying
x = -4.538894859


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.698894859, -4.538894859}

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