-12x^2+10x+17=0

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Solution for -12x^2+10x+17=0 equation: 


Simplifying
-12x2 + 10x + 17 = 0

Reorder the terms:
17 + 10x + -12x2 = 0

Solving
17 + 10x + -12x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
-1.416666667 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '1.416666667' to each side of the equation.
-1.416666667 + -0.8333333333x + 1.416666667 + x2 = 0 + 1.416666667

Reorder the terms:
-1.416666667 + 1.416666667 + -0.8333333333x + x2 = 0 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + -0.8333333333x + x2 = 0 + 1.416666667
-0.8333333333x + x2 = 0 + 1.416666667

Combine like terms: 0 + 1.416666667 = 1.416666667
-0.8333333333x + x2 = 1.416666667

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 1.416666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 1.416666667 + 0.1736111111

Combine like terms: 1.416666667 + 0.1736111111 = 1.5902777781
0.1736111111 + -0.8333333333x + x2 = 1.5902777781

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 1.5902777781

Calculate the square root of the right side: 1.261062163

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 1.261062163 and -1.261062163.


Subproblem 1
x + -0.4166666667 = 1.261062163

Simplifying
x + -0.4166666667 = 1.261062163

Reorder the terms:
-0.4166666667 + x = 1.261062163

Solving
-0.4166666667 + x = 1.261062163

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 1.261062163 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 1.261062163 + 0.4166666667
x = 1.261062163 + 0.4166666667

Combine like terms: 1.261062163 + 0.4166666667 = 1.6777288297
x = 1.6777288297

Simplifying
x = 1.6777288297


Subproblem 2
x + -0.4166666667 = -1.261062163

Simplifying
x + -0.4166666667 = -1.261062163

Reorder the terms:
-0.4166666667 + x = -1.261062163

Solving
-0.4166666667 + x = -1.261062163

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -1.261062163 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -1.261062163 + 0.4166666667
x = -1.261062163 + 0.4166666667

Combine like terms: -1.261062163 + 0.4166666667 = -0.8443954963
x = -0.8443954963

Simplifying
x = -0.8443954963


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6777288297, -0.8443954963}

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