6x^2+3x-7=0

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Solution for 6x^2+3x-7=0 equation:


Simplifying
6x2 + 3x + -7 = 0

Reorder the terms:
-7 + 3x + 6x2 = 0

Solving
-7 + 3x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-1.166666667 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 0.5x + 1.166666667 + x2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 0.5x + x2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 0.5x + x2 = 0 + 1.166666667
0.5x + x2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
0.5x + x2 = 1.166666667

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.166666667 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.166666667 + 0.0625

Combine like terms: 1.166666667 + 0.0625 = 1.229166667
0.0625 + 0.5x + x2 = 1.229166667

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.229166667

Calculate the square root of the right side: 1.108677891

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.108677891 and -1.108677891.

Subproblem 1

x + 0.25 = 1.108677891 Simplifying x + 0.25 = 1.108677891 Reorder the terms: 0.25 + x = 1.108677891 Solving 0.25 + x = 1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.108677891 + -0.25 x = 1.108677891 + -0.25 Combine like terms: 1.108677891 + -0.25 = 0.858677891 x = 0.858677891 Simplifying x = 0.858677891

Subproblem 2

x + 0.25 = -1.108677891 Simplifying x + 0.25 = -1.108677891 Reorder the terms: 0.25 + x = -1.108677891 Solving 0.25 + x = -1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.108677891 + -0.25 x = -1.108677891 + -0.25 Combine like terms: -1.108677891 + -0.25 = -1.358677891 x = -1.358677891 Simplifying x = -1.358677891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.858677891, -1.358677891}

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