12x^2+7x-21=0

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Solution for 12x^2+7x-21=0 equation:


Simplifying
12x2 + 7x + -21 = 0

Reorder the terms:
-21 + 7x + 12x2 = 0

Solving
-21 + 7x + 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'.
-1.75 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 0.5833333333x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 0.5833333333x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 0.5833333333x + x2 = 0 + 1.75
0.5833333333x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
0.5833333333x + x2 = 1.75

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 = 1.75 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 1.75 + 0.08506944446

Combine like terms: 1.75 + 0.08506944446 = 1.83506944446
0.08506944446 + 0.5833333333x + x2 = 1.83506944446

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 1.83506944446

Calculate the square root of the right side: 1.354647351

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 1.354647351 and -1.354647351.

Subproblem 1

x + 0.2916666667 = 1.354647351 Simplifying x + 0.2916666667 = 1.354647351 Reorder the terms: 0.2916666667 + x = 1.354647351 Solving 0.2916666667 + x = 1.354647351 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 = 1.354647351 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = 1.354647351 + -0.2916666667 x = 1.354647351 + -0.2916666667 Combine like terms: 1.354647351 + -0.2916666667 = 1.0629806843 x = 1.0629806843 Simplifying x = 1.0629806843

Subproblem 2

x + 0.2916666667 = -1.354647351 Simplifying x + 0.2916666667 = -1.354647351 Reorder the terms: 0.2916666667 + x = -1.354647351 Solving 0.2916666667 + x = -1.354647351 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 = -1.354647351 + -0.2916666667 Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000 0.0000000000 + x = -1.354647351 + -0.2916666667 x = -1.354647351 + -0.2916666667 Combine like terms: -1.354647351 + -0.2916666667 = -1.6463140177 x = -1.6463140177 Simplifying x = -1.6463140177

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0629806843, -1.6463140177}

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