(x^2)+(1.73x-4)=0

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Solution for (x^2)+(1.73x-4)=0 equation: 


Simplifying
(x2) + (1.73x + -4) = 0
x2 + (1.73x + -4) = 0

Reorder the terms:
x2 + (-4 + 1.73x) = 0

Remove parenthesis around (-4 + 1.73x)
x2 + -4 + 1.73x = 0

Reorder the terms:
-4 + 1.73x + x2 = 0

Solving
-4 + 1.73x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.73x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.73x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.73x + x2 = 0 + 4
1.73x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.73x + x2 = 4

The x term is 1.73x.  Take half its coefficient (0.865).
Square it (0.748225) and add it to both sides.

Add '0.748225' to each side of the equation.
1.73x + 0.748225 + x2 = 4 + 0.748225

Reorder the terms:
0.748225 + 1.73x + x2 = 4 + 0.748225

Combine like terms: 4 + 0.748225 = 4.748225
0.748225 + 1.73x + x2 = 4.748225

Factor a perfect square on the left side:
(x + 0.865)(x + 0.865) = 4.748225

Calculate the square root of the right side: 2.179042221

Break this problem into two subproblems by setting 
(x + 0.865) equal to 2.179042221 and -2.179042221.


Subproblem 1
x + 0.865 = 2.179042221

Simplifying
x + 0.865 = 2.179042221

Reorder the terms:
0.865 + x = 2.179042221

Solving
0.865 + x = 2.179042221

Solving for variable 'x'.

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

Add '-0.865' to each side of the equation.
0.865 + -0.865 + x = 2.179042221 + -0.865

Combine like terms: 0.865 + -0.865 = 0.000
0.000 + x = 2.179042221 + -0.865
x = 2.179042221 + -0.865

Combine like terms: 2.179042221 + -0.865 = 1.314042221
x = 1.314042221

Simplifying
x = 1.314042221


Subproblem 2
x + 0.865 = -2.179042221

Simplifying
x + 0.865 = -2.179042221

Reorder the terms:
0.865 + x = -2.179042221

Solving
0.865 + x = -2.179042221

Solving for variable 'x'.

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

Add '-0.865' to each side of the equation.
0.865 + -0.865 + x = -2.179042221 + -0.865

Combine like terms: 0.865 + -0.865 = 0.000
0.000 + x = -2.179042221 + -0.865
x = -2.179042221 + -0.865

Combine like terms: -2.179042221 + -0.865 = -3.044042221
x = -3.044042221

Simplifying
x = -3.044042221


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.314042221, -3.044042221}

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