-3.97x^2+17x+8.05=0

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Solution for -3.97x^2+17x+8.05=0 equation: 


Simplifying
-3.97x2 + 17x + 8.05 = 0

Reorder the terms:
8.05 + 17x + -3.97x2 = 0

Solving
8.05 + 17x + -3.97x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3.97 the coefficient of the squared term: 

Divide each side by '-3.97'.
-2.027707809 + -4.282115869x + x2 = 0

Move the constant term to the right:

Add '2.027707809' to each side of the equation.
-2.027707809 + -4.282115869x + 2.027707809 + x2 = 0 + 2.027707809

Reorder the terms:
-2.027707809 + 2.027707809 + -4.282115869x + x2 = 0 + 2.027707809

Combine like terms: -2.027707809 + 2.027707809 = 0.000000000
0.000000000 + -4.282115869x + x2 = 0 + 2.027707809
-4.282115869x + x2 = 0 + 2.027707809

Combine like terms: 0 + 2.027707809 = 2.027707809
-4.282115869x + x2 = 2.027707809

The x term is -4.282115869x.  Take half its coefficient (-2.141057935).
Square it (4.584129081) and add it to both sides.

Add '4.584129081' to each side of the equation.
-4.282115869x + 4.584129081 + x2 = 2.027707809 + 4.584129081

Reorder the terms:
4.584129081 + -4.282115869x + x2 = 2.027707809 + 4.584129081

Combine like terms: 2.027707809 + 4.584129081 = 6.61183689
4.584129081 + -4.282115869x + x2 = 6.61183689

Factor a perfect square on the left side:
(x + -2.141057935)(x + -2.141057935) = 6.61183689

Calculate the square root of the right side: 2.571349235

Break this problem into two subproblems by setting 
(x + -2.141057935) equal to 2.571349235 and -2.571349235.


Subproblem 1
x + -2.141057935 = 2.571349235

Simplifying
x + -2.141057935 = 2.571349235

Reorder the terms:
-2.141057935 + x = 2.571349235

Solving
-2.141057935 + x = 2.571349235

Solving for variable 'x'.

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

Add '2.141057935' to each side of the equation.
-2.141057935 + 2.141057935 + x = 2.571349235 + 2.141057935

Combine like terms: -2.141057935 + 2.141057935 = 0.000000000
0.000000000 + x = 2.571349235 + 2.141057935
x = 2.571349235 + 2.141057935

Combine like terms: 2.571349235 + 2.141057935 = 4.71240717
x = 4.71240717

Simplifying
x = 4.71240717


Subproblem 2
x + -2.141057935 = -2.571349235

Simplifying
x + -2.141057935 = -2.571349235

Reorder the terms:
-2.141057935 + x = -2.571349235

Solving
-2.141057935 + x = -2.571349235

Solving for variable 'x'.

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

Add '2.141057935' to each side of the equation.
-2.141057935 + 2.141057935 + x = -2.571349235 + 2.141057935

Combine like terms: -2.141057935 + 2.141057935 = 0.000000000
0.000000000 + x = -2.571349235 + 2.141057935
x = -2.571349235 + 2.141057935

Combine like terms: -2.571349235 + 2.141057935 = -0.4302913
x = -0.4302913

Simplifying
x = -0.4302913


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.71240717, -0.4302913}

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