15-0.8x+0.12x^2=17

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Solution for 15-0.8x+0.12x^2=17 equation: 


Simplifying
15 + -0.8x + 0.12x2 = 17

Solving
15 + -0.8x + 0.12x2 = 17

Solving for variable 'x'.

Reorder the terms:
15 + -17 + -0.8x + 0.12x2 = 17 + -17

Combine like terms: 15 + -17 = -2
-2 + -0.8x + 0.12x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-2 + -0.8x + 0.12x2 = 0

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

Divide each side by '0.12'.
-16.66666667 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -6.666666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -6.666666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -6.666666667x + x2 = 0 + 16.66666667
-6.666666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-6.666666667x + x2 = 16.66666667

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 16.66666667 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 16.66666667 + 11.11111112

Combine like terms: 16.66666667 + 11.11111112 = 27.77777779
11.11111112 + -6.666666667x + x2 = 27.77777779

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 27.77777779

Calculate the square root of the right side: 5.270462768

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 5.270462768 and -5.270462768.


Subproblem 1
x + -3.333333334 = 5.270462768

Simplifying
x + -3.333333334 = 5.270462768

Reorder the terms:
-3.333333334 + x = 5.270462768

Solving
-3.333333334 + x = 5.270462768

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 5.270462768 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 5.270462768 + 3.333333334
x = 5.270462768 + 3.333333334

Combine like terms: 5.270462768 + 3.333333334 = 8.603796102
x = 8.603796102

Simplifying
x = 8.603796102


Subproblem 2
x + -3.333333334 = -5.270462768

Simplifying
x + -3.333333334 = -5.270462768

Reorder the terms:
-3.333333334 + x = -5.270462768

Solving
-3.333333334 + x = -5.270462768

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -5.270462768 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -5.270462768 + 3.333333334
x = -5.270462768 + 3.333333334

Combine like terms: -5.270462768 + 3.333333334 = -1.937129434
x = -1.937129434

Simplifying
x = -1.937129434


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.603796102, -1.937129434}

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