12x^2+17x-3=0

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Solution for 12x^2+17x-3=0 equation:


Simplifying
12x2 + 17x + -3 = 0

Reorder the terms:
-3 + 17x + 12x2 = 0

Solving
-3 + 17x + 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'.
-0.25 + 1.416666667x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.416666667x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.416666667x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.416666667x + x2 = 0 + 0.25
1.416666667x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.416666667x + x2 = 0.25

The x term is 1.416666667x.  Take half its coefficient (0.7083333335).
Square it (0.5017361113) and add it to both sides.

Add '0.5017361113' to each side of the equation.
1.416666667x + 0.5017361113 + x2 = 0.25 + 0.5017361113

Reorder the terms:
0.5017361113 + 1.416666667x + x2 = 0.25 + 0.5017361113

Combine like terms: 0.25 + 0.5017361113 = 0.7517361113
0.5017361113 + 1.416666667x + x2 = 0.7517361113

Factor a perfect square on the left side:
(x + 0.7083333335)(x + 0.7083333335) = 0.7517361113

Calculate the square root of the right side: 0.867027169

Break this problem into two subproblems by setting 
(x + 0.7083333335) equal to 0.867027169 and -0.867027169.

Subproblem 1

x + 0.7083333335 = 0.867027169 Simplifying x + 0.7083333335 = 0.867027169 Reorder the terms: 0.7083333335 + x = 0.867027169 Solving 0.7083333335 + x = 0.867027169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = 0.867027169 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = 0.867027169 + -0.7083333335 x = 0.867027169 + -0.7083333335 Combine like terms: 0.867027169 + -0.7083333335 = 0.1586938355 x = 0.1586938355 Simplifying x = 0.1586938355

Subproblem 2

x + 0.7083333335 = -0.867027169 Simplifying x + 0.7083333335 = -0.867027169 Reorder the terms: 0.7083333335 + x = -0.867027169 Solving 0.7083333335 + x = -0.867027169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7083333335' to each side of the equation. 0.7083333335 + -0.7083333335 + x = -0.867027169 + -0.7083333335 Combine like terms: 0.7083333335 + -0.7083333335 = 0.0000000000 0.0000000000 + x = -0.867027169 + -0.7083333335 x = -0.867027169 + -0.7083333335 Combine like terms: -0.867027169 + -0.7083333335 = -1.5753605025 x = -1.5753605025 Simplifying x = -1.5753605025

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1586938355, -1.5753605025}

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