7x^2-2x-13=0

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Solution for 7x^2-2x-13=0 equation:


Simplifying
7x2 + -2x + -13 = 0

Reorder the terms:
-13 + -2x + 7x2 = 0

Solving
-13 + -2x + 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'.
-1.857142857 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + -0.2857142857x + 1.857142857 + x2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + -0.2857142857x + x2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + -0.2857142857x + x2 = 0 + 1.857142857
-0.2857142857x + x2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
-0.2857142857x + x2 = 1.857142857

The x term is -0.2857142857x.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857x + 0.02040816328 + x2 = 1.857142857 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 1.857142857 + 0.02040816328

Combine like terms: 1.857142857 + 0.02040816328 = 1.87755102028
0.02040816328 + -0.2857142857x + x2 = 1.87755102028

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 1.87755102028

Calculate the square root of the right side: 1.370237578

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 1.370237578 and -1.370237578.

Subproblem 1

x + -0.1428571429 = 1.370237578 Simplifying x + -0.1428571429 = 1.370237578 Reorder the terms: -0.1428571429 + x = 1.370237578 Solving -0.1428571429 + x = 1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 1.370237578 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.370237578 + 0.1428571429 x = 1.370237578 + 0.1428571429 Combine like terms: 1.370237578 + 0.1428571429 = 1.5130947209 x = 1.5130947209 Simplifying x = 1.5130947209

Subproblem 2

x + -0.1428571429 = -1.370237578 Simplifying x + -0.1428571429 = -1.370237578 Reorder the terms: -0.1428571429 + x = -1.370237578 Solving -0.1428571429 + x = -1.370237578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -1.370237578 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.370237578 + 0.1428571429 x = -1.370237578 + 0.1428571429 Combine like terms: -1.370237578 + 0.1428571429 = -1.2273804351 x = -1.2273804351 Simplifying x = -1.2273804351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5130947209, -1.2273804351}

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