7x^2-6x-12=0

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Solution for 7x^2-6x-12=0 equation:


Simplifying
7x2 + -6x + -12 = 0

Reorder the terms:
-12 + -6x + 7x2 = 0

Solving
-12 + -6x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-1.714285714 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + -0.8571428571x + 1.714285714 + x2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + -0.8571428571x + x2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + -0.8571428571x + x2 = 0 + 1.714285714
-0.8571428571x + x2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
-0.8571428571x + x2 = 1.714285714

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 1.714285714 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 1.714285714 + 0.1836734694

Combine like terms: 1.714285714 + 0.1836734694 = 1.8979591834
0.1836734694 + -0.8571428571x + x2 = 1.8979591834

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 1.8979591834

Calculate the square root of the right side: 1.377664394

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 1.377664394 and -1.377664394.

Subproblem 1

x + -0.4285714286 = 1.377664394 Simplifying x + -0.4285714286 = 1.377664394 Reorder the terms: -0.4285714286 + x = 1.377664394 Solving -0.4285714286 + x = 1.377664394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.377664394 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.377664394 + 0.4285714286 x = 1.377664394 + 0.4285714286 Combine like terms: 1.377664394 + 0.4285714286 = 1.8062358226 x = 1.8062358226 Simplifying x = 1.8062358226

Subproblem 2

x + -0.4285714286 = -1.377664394 Simplifying x + -0.4285714286 = -1.377664394 Reorder the terms: -0.4285714286 + x = -1.377664394 Solving -0.4285714286 + x = -1.377664394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.377664394 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.377664394 + 0.4285714286 x = -1.377664394 + 0.4285714286 Combine like terms: -1.377664394 + 0.4285714286 = -0.9490929654 x = -0.9490929654 Simplifying x = -0.9490929654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8062358226, -0.9490929654}

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