17x^2-22x+6=0

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Solution for 17x^2-22x+6=0 equation:


Simplifying
17x2 + -22x + 6 = 0

Reorder the terms:
6 + -22x + 17x2 = 0

Solving
6 + -22x + 17x2 = 0

Solving for variable 'x'.

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

Divide each side by '17'.
0.3529411765 + -1.294117647x + x2 = 0

Move the constant term to the right:

Add '-0.3529411765' to each side of the equation.
0.3529411765 + -1.294117647x + -0.3529411765 + x2 = 0 + -0.3529411765

Reorder the terms:
0.3529411765 + -0.3529411765 + -1.294117647x + x2 = 0 + -0.3529411765

Combine like terms: 0.3529411765 + -0.3529411765 = 0.0000000000
0.0000000000 + -1.294117647x + x2 = 0 + -0.3529411765
-1.294117647x + x2 = 0 + -0.3529411765

Combine like terms: 0 + -0.3529411765 = -0.3529411765
-1.294117647x + x2 = -0.3529411765

The x term is -1.294117647x.  Take half its coefficient (-0.6470588235).
Square it (0.4186851211) and add it to both sides.

Add '0.4186851211' to each side of the equation.
-1.294117647x + 0.4186851211 + x2 = -0.3529411765 + 0.4186851211

Reorder the terms:
0.4186851211 + -1.294117647x + x2 = -0.3529411765 + 0.4186851211

Combine like terms: -0.3529411765 + 0.4186851211 = 0.0657439446
0.4186851211 + -1.294117647x + x2 = 0.0657439446

Factor a perfect square on the left side:
(x + -0.6470588235)(x + -0.6470588235) = 0.0657439446

Calculate the square root of the right side: 0.25640582

Break this problem into two subproblems by setting 
(x + -0.6470588235) equal to 0.25640582 and -0.25640582.

Subproblem 1

x + -0.6470588235 = 0.25640582 Simplifying x + -0.6470588235 = 0.25640582 Reorder the terms: -0.6470588235 + x = 0.25640582 Solving -0.6470588235 + x = 0.25640582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6470588235' to each side of the equation. -0.6470588235 + 0.6470588235 + x = 0.25640582 + 0.6470588235 Combine like terms: -0.6470588235 + 0.6470588235 = 0.0000000000 0.0000000000 + x = 0.25640582 + 0.6470588235 x = 0.25640582 + 0.6470588235 Combine like terms: 0.25640582 + 0.6470588235 = 0.9034646435 x = 0.9034646435 Simplifying x = 0.9034646435

Subproblem 2

x + -0.6470588235 = -0.25640582 Simplifying x + -0.6470588235 = -0.25640582 Reorder the terms: -0.6470588235 + x = -0.25640582 Solving -0.6470588235 + x = -0.25640582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6470588235' to each side of the equation. -0.6470588235 + 0.6470588235 + x = -0.25640582 + 0.6470588235 Combine like terms: -0.6470588235 + 0.6470588235 = 0.0000000000 0.0000000000 + x = -0.25640582 + 0.6470588235 x = -0.25640582 + 0.6470588235 Combine like terms: -0.25640582 + 0.6470588235 = 0.3906530035 x = 0.3906530035 Simplifying x = 0.3906530035

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9034646435, 0.3906530035}

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