13x^2+12x-96=0

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Solution for 13x^2+12x-96=0 equation:


Simplifying
13x2 + 12x + -96 = 0

Reorder the terms:
-96 + 12x + 13x2 = 0

Solving
-96 + 12x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-7.384615385 + 0.9230769231x + x2 = 0

Move the constant term to the right:

Add '7.384615385' to each side of the equation.
-7.384615385 + 0.9230769231x + 7.384615385 + x2 = 0 + 7.384615385

Reorder the terms:
-7.384615385 + 7.384615385 + 0.9230769231x + x2 = 0 + 7.384615385

Combine like terms: -7.384615385 + 7.384615385 = 0.000000000
0.000000000 + 0.9230769231x + x2 = 0 + 7.384615385
0.9230769231x + x2 = 0 + 7.384615385

Combine like terms: 0 + 7.384615385 = 7.384615385
0.9230769231x + x2 = 7.384615385

The x term is 0.9230769231x.  Take half its coefficient (0.4615384616).
Square it (0.2130177515) and add it to both sides.

Add '0.2130177515' to each side of the equation.
0.9230769231x + 0.2130177515 + x2 = 7.384615385 + 0.2130177515

Reorder the terms:
0.2130177515 + 0.9230769231x + x2 = 7.384615385 + 0.2130177515

Combine like terms: 7.384615385 + 0.2130177515 = 7.5976331365
0.2130177515 + 0.9230769231x + x2 = 7.5976331365

Factor a perfect square on the left side:
(x + 0.4615384616)(x + 0.4615384616) = 7.5976331365

Calculate the square root of the right side: 2.756380441

Break this problem into two subproblems by setting 
(x + 0.4615384616) equal to 2.756380441 and -2.756380441.

Subproblem 1

x + 0.4615384616 = 2.756380441 Simplifying x + 0.4615384616 = 2.756380441 Reorder the terms: 0.4615384616 + x = 2.756380441 Solving 0.4615384616 + x = 2.756380441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = 2.756380441 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = 2.756380441 + -0.4615384616 x = 2.756380441 + -0.4615384616 Combine like terms: 2.756380441 + -0.4615384616 = 2.2948419794 x = 2.2948419794 Simplifying x = 2.2948419794

Subproblem 2

x + 0.4615384616 = -2.756380441 Simplifying x + 0.4615384616 = -2.756380441 Reorder the terms: 0.4615384616 + x = -2.756380441 Solving 0.4615384616 + x = -2.756380441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = -2.756380441 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = -2.756380441 + -0.4615384616 x = -2.756380441 + -0.4615384616 Combine like terms: -2.756380441 + -0.4615384616 = -3.2179189026 x = -3.2179189026 Simplifying x = -3.2179189026

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2948419794, -3.2179189026}

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