13x*x-41x-130=0

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Solution for 13x*x-41x-130=0 equation:


Simplifying
13x * x + -41x + -130 = 0

Multiply x * x
13x2 + -41x + -130 = 0

Reorder the terms:
-130 + -41x + 13x2 = 0

Solving
-130 + -41x + 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'.
-10 + -3.153846154x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -3.153846154x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -3.153846154x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3.153846154x + x2 = 0 + 10
-3.153846154x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-3.153846154x + x2 = 10

The x term is -3.153846154x.  Take half its coefficient (-1.576923077).
Square it (2.486686391) and add it to both sides.

Add '2.486686391' to each side of the equation.
-3.153846154x + 2.486686391 + x2 = 10 + 2.486686391

Reorder the terms:
2.486686391 + -3.153846154x + x2 = 10 + 2.486686391

Combine like terms: 10 + 2.486686391 = 12.486686391
2.486686391 + -3.153846154x + x2 = 12.486686391

Factor a perfect square on the left side:
(x + -1.576923077)(x + -1.576923077) = 12.486686391

Calculate the square root of the right side: 3.533650576

Break this problem into two subproblems by setting 
(x + -1.576923077) equal to 3.533650576 and -3.533650576.

Subproblem 1

x + -1.576923077 = 3.533650576 Simplifying x + -1.576923077 = 3.533650576 Reorder the terms: -1.576923077 + x = 3.533650576 Solving -1.576923077 + x = 3.533650576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.576923077' to each side of the equation. -1.576923077 + 1.576923077 + x = 3.533650576 + 1.576923077 Combine like terms: -1.576923077 + 1.576923077 = 0.000000000 0.000000000 + x = 3.533650576 + 1.576923077 x = 3.533650576 + 1.576923077 Combine like terms: 3.533650576 + 1.576923077 = 5.110573653 x = 5.110573653 Simplifying x = 5.110573653

Subproblem 2

x + -1.576923077 = -3.533650576 Simplifying x + -1.576923077 = -3.533650576 Reorder the terms: -1.576923077 + x = -3.533650576 Solving -1.576923077 + x = -3.533650576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.576923077' to each side of the equation. -1.576923077 + 1.576923077 + x = -3.533650576 + 1.576923077 Combine like terms: -1.576923077 + 1.576923077 = 0.000000000 0.000000000 + x = -3.533650576 + 1.576923077 x = -3.533650576 + 1.576923077 Combine like terms: -3.533650576 + 1.576923077 = -1.956727499 x = -1.956727499 Simplifying x = -1.956727499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.110573653, -1.956727499}

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