12x^2+7x-5=-3

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Solution for 12x^2+7x-5=-3 equation: 


Simplifying
12x2 + 7x + -5 = -3

Reorder the terms:
-5 + 7x + 12x2 = -3

Solving
-5 + 7x + 12x2 = -3

Solving for variable 'x'.

Reorder the terms:
-5 + 3 + 7x + 12x2 = -3 + 3

Combine like terms: -5 + 3 = -2
-2 + 7x + 12x2 = -3 + 3

Combine like terms: -3 + 3 = 0
-2 + 7x + 12x2 = 0

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

Divide each side by '12'.
-0.1666666667 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.5833333333x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 0.5833333333x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 0.5833333333x + x2 = 0 + 0.1666666667
0.5833333333x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
0.5833333333x + x2 = 0.1666666667

The x term is 0.5833333333x.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333x + 0.08506944446 + x2 = 0.1666666667 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 0.1666666667 + 0.08506944446

Combine like terms: 0.1666666667 + 0.08506944446 = 0.25173611116
0.08506944446 + 0.5833333333x + x2 = 0.25173611116

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 0.25173611116

Calculate the square root of the right side: 0.501733107

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 0.501733107 and -0.501733107.


Subproblem 1
x + 0.2916666667 = 0.501733107

Simplifying
x + 0.2916666667 = 0.501733107

Reorder the terms:
0.2916666667 + x = 0.501733107

Solving
0.2916666667 + x = 0.501733107

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = 0.501733107 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = 0.501733107 + -0.2916666667
x = 0.501733107 + -0.2916666667

Combine like terms: 0.501733107 + -0.2916666667 = 0.2100664403
x = 0.2100664403

Simplifying
x = 0.2100664403


Subproblem 2
x + 0.2916666667 = -0.501733107

Simplifying
x + 0.2916666667 = -0.501733107

Reorder the terms:
0.2916666667 + x = -0.501733107

Solving
0.2916666667 + x = -0.501733107

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = -0.501733107 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = -0.501733107 + -0.2916666667
x = -0.501733107 + -0.2916666667

Combine like terms: -0.501733107 + -0.2916666667 = -0.7933997737
x = -0.7933997737

Simplifying
x = -0.7933997737


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2100664403, -0.7933997737}

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