-0.6x^2+4.6x+3=0

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Solution for -0.6x^2+4.6x+3=0 equation: 


Simplifying
-0.6x2 + 4.6x + 3 = 0

Reorder the terms:
3 + 4.6x + -0.6x2 = 0

Solving
3 + 4.6x + -0.6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.6 the coefficient of the squared term: 

Divide each side by '-0.6'.
-5 + -7.666666667x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -7.666666667x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -7.666666667x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7.666666667x + x2 = 0 + 5
-7.666666667x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-7.666666667x + x2 = 5

The x term is -7.666666667x.  Take half its coefficient (-3.833333334).
Square it (14.69444445) and add it to both sides.

Add '14.69444445' to each side of the equation.
-7.666666667x + 14.69444445 + x2 = 5 + 14.69444445

Reorder the terms:
14.69444445 + -7.666666667x + x2 = 5 + 14.69444445

Combine like terms: 5 + 14.69444445 = 19.69444445
14.69444445 + -7.666666667x + x2 = 19.69444445

Factor a perfect square on the left side:
(x + -3.833333334)(x + -3.833333334) = 19.69444445

Calculate the square root of the right side: 4.437842319

Break this problem into two subproblems by setting 
(x + -3.833333334) equal to 4.437842319 and -4.437842319.


Subproblem 1
x + -3.833333334 = 4.437842319

Simplifying
x + -3.833333334 = 4.437842319

Reorder the terms:
-3.833333334 + x = 4.437842319

Solving
-3.833333334 + x = 4.437842319

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = 4.437842319 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = 4.437842319 + 3.833333334
x = 4.437842319 + 3.833333334

Combine like terms: 4.437842319 + 3.833333334 = 8.271175653
x = 8.271175653

Simplifying
x = 8.271175653


Subproblem 2
x + -3.833333334 = -4.437842319

Simplifying
x + -3.833333334 = -4.437842319

Reorder the terms:
-3.833333334 + x = -4.437842319

Solving
-3.833333334 + x = -4.437842319

Solving for variable 'x'.

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

Add '3.833333334' to each side of the equation.
-3.833333334 + 3.833333334 + x = -4.437842319 + 3.833333334

Combine like terms: -3.833333334 + 3.833333334 = 0.000000000
0.000000000 + x = -4.437842319 + 3.833333334
x = -4.437842319 + 3.833333334

Combine like terms: -4.437842319 + 3.833333334 = -0.604508985
x = -0.604508985

Simplifying
x = -0.604508985


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.271175653, -0.604508985}

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