6x^2+16x+8=1

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Solution for 6x^2+16x+8=1 equation:


Simplifying
6x2 + 16x + 8 = 1

Reorder the terms:
8 + 16x + 6x2 = 1

Solving
8 + 16x + 6x2 = 1

Solving for variable 'x'.

Reorder the terms:
8 + -1 + 16x + 6x2 = 1 + -1

Combine like terms: 8 + -1 = 7
7 + 16x + 6x2 = 1 + -1

Combine like terms: 1 + -1 = 0
7 + 16x + 6x2 = 0

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

Divide each side by '6'.
1.166666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + 2.666666667x + -1.166666667 + x2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + 2.666666667x + x2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -1.166666667
2.666666667x + x2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
2.666666667x + x2 = -1.166666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -1.166666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -1.166666667 + 1.777777780

Combine like terms: -1.166666667 + 1.777777780 = 0.611111113
1.777777780 + 2.666666667x + x2 = 0.611111113

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 0.611111113

Calculate the square root of the right side: 0.781735961

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 0.781735961 and -0.781735961.

Subproblem 1

x + 1.333333334 = 0.781735961 Simplifying x + 1.333333334 = 0.781735961 Reorder the terms: 1.333333334 + x = 0.781735961 Solving 1.333333334 + x = 0.781735961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 0.781735961 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 0.781735961 + -1.333333334 x = 0.781735961 + -1.333333334 Combine like terms: 0.781735961 + -1.333333334 = -0.551597373 x = -0.551597373 Simplifying x = -0.551597373

Subproblem 2

x + 1.333333334 = -0.781735961 Simplifying x + 1.333333334 = -0.781735961 Reorder the terms: 1.333333334 + x = -0.781735961 Solving 1.333333334 + x = -0.781735961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -0.781735961 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -0.781735961 + -1.333333334 x = -0.781735961 + -1.333333334 Combine like terms: -0.781735961 + -1.333333334 = -2.115069295 x = -2.115069295 Simplifying x = -2.115069295

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.551597373, -2.115069295}

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