x^2+3.4x-6=0

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Solution for x^2+3.4x-6=0 equation: 


Simplifying
x2 + 3.4x + -6 = 0

Reorder the terms:
-6 + 3.4x + x2 = 0

Solving
-6 + 3.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.4x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.4x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.4x + x2 = 0 + 6
3.4x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.4x + x2 = 6

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = 6 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 6 + 2.89

Combine like terms: 6 + 2.89 = 8.89
2.89 + 3.4x + x2 = 8.89

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 8.89

Calculate the square root of the right side: 2.981610303

Break this problem into two subproblems by setting 
(x + 1.7) equal to 2.981610303 and -2.981610303.


Subproblem 1
x + 1.7 = 2.981610303

Simplifying
x + 1.7 = 2.981610303

Reorder the terms:
1.7 + x = 2.981610303

Solving
1.7 + x = 2.981610303

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 2.981610303 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 2.981610303 + -1.7
x = 2.981610303 + -1.7

Combine like terms: 2.981610303 + -1.7 = 1.281610303
x = 1.281610303

Simplifying
x = 1.281610303


Subproblem 2
x + 1.7 = -2.981610303

Simplifying
x + 1.7 = -2.981610303

Reorder the terms:
1.7 + x = -2.981610303

Solving
1.7 + x = -2.981610303

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -2.981610303 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -2.981610303 + -1.7
x = -2.981610303 + -1.7

Combine like terms: -2.981610303 + -1.7 = -4.681610303
x = -4.681610303

Simplifying
x = -4.681610303


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.281610303, -4.681610303}

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