-0.2x^2+9.7x+1=0

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Solution for -0.2x^2+9.7x+1=0 equation: 


Simplifying
-0.2x2 + 9.7x + 1 = 0

Reorder the terms:
1 + 9.7x + -0.2x2 = 0

Solving
1 + 9.7x + -0.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-5 + -48.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -48.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -48.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -48.5x + x2 = 0 + 5
-48.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-48.5x + x2 = 5

The x term is -48.5x.  Take half its coefficient (-24.25).
Square it (588.0625) and add it to both sides.

Add '588.0625' to each side of the equation.
-48.5x + 588.0625 + x2 = 5 + 588.0625

Reorder the terms:
588.0625 + -48.5x + x2 = 5 + 588.0625

Combine like terms: 5 + 588.0625 = 593.0625
588.0625 + -48.5x + x2 = 593.0625

Factor a perfect square on the left side:
(x + -24.25)(x + -24.25) = 593.0625

Calculate the square root of the right side: 24.352874574

Break this problem into two subproblems by setting 
(x + -24.25) equal to 24.352874574 and -24.352874574.


Subproblem 1
x + -24.25 = 24.352874574

Simplifying
x + -24.25 = 24.352874574

Reorder the terms:
-24.25 + x = 24.352874574

Solving
-24.25 + x = 24.352874574

Solving for variable 'x'.

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

Add '24.25' to each side of the equation.
-24.25 + 24.25 + x = 24.352874574 + 24.25

Combine like terms: -24.25 + 24.25 = 0.00
0.00 + x = 24.352874574 + 24.25
x = 24.352874574 + 24.25

Combine like terms: 24.352874574 + 24.25 = 48.602874574
x = 48.602874574

Simplifying
x = 48.602874574


Subproblem 2
x + -24.25 = -24.352874574

Simplifying
x + -24.25 = -24.352874574

Reorder the terms:
-24.25 + x = -24.352874574

Solving
-24.25 + x = -24.352874574

Solving for variable 'x'.

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

Add '24.25' to each side of the equation.
-24.25 + 24.25 + x = -24.352874574 + 24.25

Combine like terms: -24.25 + 24.25 = 0.00
0.00 + x = -24.352874574 + 24.25
x = -24.352874574 + 24.25

Combine like terms: -24.352874574 + 24.25 = -0.102874574
x = -0.102874574

Simplifying
x = -0.102874574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.602874574, -0.102874574}

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