-2x-3+6x+14x^2-9x=1

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Solution for -2x-3+6x+14x^2-9x=1 equation:


Simplifying
-2x + -3 + 6x + 14x2 + -9x = 1

Reorder the terms:
-3 + -2x + 6x + -9x + 14x2 = 1

Combine like terms: -2x + 6x = 4x
-3 + 4x + -9x + 14x2 = 1

Combine like terms: 4x + -9x = -5x
-3 + -5x + 14x2 = 1

Solving
-3 + -5x + 14x2 = 1

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + -5x + 14x2 = 1 + -1

Combine like terms: -3 + -1 = -4
-4 + -5x + 14x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-4 + -5x + 14x2 = 0

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

Divide each side by '14'.
-0.2857142857 + -0.3571428571x + x2 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + -0.3571428571x + 0.2857142857 + x2 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + -0.3571428571x + x2 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + -0.3571428571x + x2 = 0 + 0.2857142857
-0.3571428571x + x2 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
-0.3571428571x + x2 = 0.2857142857

The x term is -0.3571428571x.  Take half its coefficient (-0.1785714286).
Square it (0.03188775511) and add it to both sides.

Add '0.03188775511' to each side of the equation.
-0.3571428571x + 0.03188775511 + x2 = 0.2857142857 + 0.03188775511

Reorder the terms:
0.03188775511 + -0.3571428571x + x2 = 0.2857142857 + 0.03188775511

Combine like terms: 0.2857142857 + 0.03188775511 = 0.31760204081
0.03188775511 + -0.3571428571x + x2 = 0.31760204081

Factor a perfect square on the left side:
(x + -0.1785714286)(x + -0.1785714286) = 0.31760204081

Calculate the square root of the right side: 0.563561923

Break this problem into two subproblems by setting 
(x + -0.1785714286) equal to 0.563561923 and -0.563561923.

Subproblem 1

x + -0.1785714286 = 0.563561923 Simplifying x + -0.1785714286 = 0.563561923 Reorder the terms: -0.1785714286 + x = 0.563561923 Solving -0.1785714286 + x = 0.563561923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = 0.563561923 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = 0.563561923 + 0.1785714286 x = 0.563561923 + 0.1785714286 Combine like terms: 0.563561923 + 0.1785714286 = 0.7421333516 x = 0.7421333516 Simplifying x = 0.7421333516

Subproblem 2

x + -0.1785714286 = -0.563561923 Simplifying x + -0.1785714286 = -0.563561923 Reorder the terms: -0.1785714286 + x = -0.563561923 Solving -0.1785714286 + x = -0.563561923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.1785714286 + x = -0.563561923 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x = -0.563561923 + 0.1785714286 x = -0.563561923 + 0.1785714286 Combine like terms: -0.563561923 + 0.1785714286 = -0.3849904944 x = -0.3849904944 Simplifying x = -0.3849904944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7421333516, -0.3849904944}

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