7x^2-7x=1

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Solution for 7x^2-7x=1 equation:


Simplifying
7x2 + -7x = 1

Reorder the terms:
-7x + 7x2 = 1

Solving
-7x + 7x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -7x + 7x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -7x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + -1x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -1x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -1x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.1428571429
-1x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-1x + x2 = 0.1428571429

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.1428571429 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.1428571429 + 0.25

Combine like terms: 0.1428571429 + 0.25 = 0.3928571429
0.25 + -1x + x2 = 0.3928571429

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.3928571429

Calculate the square root of the right side: 0.626783171

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.626783171 and -0.626783171.

Subproblem 1

x + -0.5 = 0.626783171 Simplifying x + -0.5 = 0.626783171 Reorder the terms: -0.5 + x = 0.626783171 Solving -0.5 + x = 0.626783171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.626783171 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.626783171 + 0.5 x = 0.626783171 + 0.5 Combine like terms: 0.626783171 + 0.5 = 1.126783171 x = 1.126783171 Simplifying x = 1.126783171

Subproblem 2

x + -0.5 = -0.626783171 Simplifying x + -0.5 = -0.626783171 Reorder the terms: -0.5 + x = -0.626783171 Solving -0.5 + x = -0.626783171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.626783171 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.626783171 + 0.5 x = -0.626783171 + 0.5 Combine like terms: -0.626783171 + 0.5 = -0.126783171 x = -0.126783171 Simplifying x = -0.126783171

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.126783171, -0.126783171}

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