7x^2-2x-7=0

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


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

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

Solving
-7 + -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 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.2857142857x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.2857142857x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.2857142857x + x2 = 0 + 1
-0.2857142857x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.2857142857x + x2 = 1

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 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 1 + 0.02040816328

Combine like terms: 1 + 0.02040816328 = 1.02040816328
0.02040816328 + -0.2857142857x + x2 = 1.02040816328

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 1.02040816328

Calculate the square root of the right side: 1.010152545

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 1.010152545 and -1.010152545.

Subproblem 1

x + -0.1428571429 = 1.010152545 Simplifying x + -0.1428571429 = 1.010152545 Reorder the terms: -0.1428571429 + x = 1.010152545 Solving -0.1428571429 + x = 1.010152545 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 = 1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.010152545 + 0.1428571429 x = 1.010152545 + 0.1428571429 Combine like terms: 1.010152545 + 0.1428571429 = 1.1530096879 x = 1.1530096879 Simplifying x = 1.1530096879

Subproblem 2

x + -0.1428571429 = -1.010152545 Simplifying x + -0.1428571429 = -1.010152545 Reorder the terms: -0.1428571429 + x = -1.010152545 Solving -0.1428571429 + x = -1.010152545 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 = -1.010152545 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.010152545 + 0.1428571429 x = -1.010152545 + 0.1428571429 Combine like terms: -1.010152545 + 0.1428571429 = -0.8672954021 x = -0.8672954021 Simplifying x = -0.8672954021

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1530096879, -0.8672954021}

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