7x^2=x+1

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


Simplifying
7x2 = x + 1

Reorder the terms:
7x2 = 1 + x

Solving
7x2 = 1 + x

Solving for variable 'x'.

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

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

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.1428571429 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.1428571429 + 0.005102040819

Combine like terms: 0.1428571429 + 0.005102040819 = 0.147959183719
0.005102040819 + -0.1428571429x + x2 = 0.147959183719

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.147959183719

Calculate the square root of the right side: 0.384654629

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.384654629 and -0.384654629.

Subproblem 1

x + -0.07142857145 = 0.384654629 Simplifying x + -0.07142857145 = 0.384654629 Reorder the terms: -0.07142857145 + x = 0.384654629 Solving -0.07142857145 + x = 0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.384654629 + 0.07142857145 x = 0.384654629 + 0.07142857145 Combine like terms: 0.384654629 + 0.07142857145 = 0.45608320045 x = 0.45608320045 Simplifying x = 0.45608320045

Subproblem 2

x + -0.07142857145 = -0.384654629 Simplifying x + -0.07142857145 = -0.384654629 Reorder the terms: -0.07142857145 + x = -0.384654629 Solving -0.07142857145 + x = -0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.384654629 + 0.07142857145 x = -0.384654629 + 0.07142857145 Combine like terms: -0.384654629 + 0.07142857145 = -0.31322605755 x = -0.31322605755 Simplifying x = -0.31322605755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.45608320045, -0.31322605755}

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