17x-8=3x^2

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Solution for 17x-8=3x^2 equation: 


Simplifying
17x + -8 = 3x2

Reorder the terms:
-8 + 17x = 3x2

Solving
-8 + 17x = 3x2

Solving for variable 'x'.

Combine like terms: 3x2 + -3x2 = 0
-8 + 17x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
2.666666667 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -5.666666667x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -5.666666667x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -5.666666667x + x2 = 0 + -2.666666667
-5.666666667x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-5.666666667x + x2 = -2.666666667

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = -2.666666667 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = -2.666666667 + 8.027777782

Combine like terms: -2.666666667 + 8.027777782 = 5.361111115
8.027777782 + -5.666666667x + x2 = 5.361111115

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 5.361111115

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.315407332 and -2.315407332.


Subproblem 1
x + -2.833333334 = 2.315407332

Simplifying
x + -2.833333334 = 2.315407332

Reorder the terms:
-2.833333334 + x = 2.315407332

Solving
-2.833333334 + x = 2.315407332

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = 2.315407332 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = 2.315407332 + 2.833333334
x = 2.315407332 + 2.833333334

Combine like terms: 2.315407332 + 2.833333334 = 5.148740666
x = 5.148740666

Simplifying
x = 5.148740666


Subproblem 2
x + -2.833333334 = -2.315407332

Simplifying
x + -2.833333334 = -2.315407332

Reorder the terms:
-2.833333334 + x = -2.315407332

Solving
-2.833333334 + x = -2.315407332

Solving for variable 'x'.

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

Add '2.833333334' to each side of the equation.
-2.833333334 + 2.833333334 + x = -2.315407332 + 2.833333334

Combine like terms: -2.833333334 + 2.833333334 = 0.000000000
0.000000000 + x = -2.315407332 + 2.833333334
x = -2.315407332 + 2.833333334

Combine like terms: -2.315407332 + 2.833333334 = 0.517926002
x = 0.517926002

Simplifying
x = 0.517926002


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.148740666, 0.517926002}

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