x(7x-2)=8

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Solution for x(7x-2)=8 equation:


Simplifying
x(7x + -2) = 8

Reorder the terms:
x(-2 + 7x) = 8
(-2 * x + 7x * x) = 8
(-2x + 7x2) = 8

Solving
-2x + 7x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -2x + 7x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -2x + 7x2 = 0

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

Divide each side by '7'.
-1.142857143 + -0.2857142857x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -0.2857142857x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -0.2857142857x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -0.2857142857x + x2 = 0 + 1.142857143
-0.2857142857x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-0.2857142857x + x2 = 1.142857143

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 = 1.142857143 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857x + x2 = 1.142857143 + 0.02040816328

Combine like terms: 1.142857143 + 0.02040816328 = 1.16326530628
0.02040816328 + -0.2857142857x + x2 = 1.16326530628

Factor a perfect square on the left side:
(x + -0.1428571429)(x + -0.1428571429) = 1.16326530628

Calculate the square root of the right side: 1.078547777

Break this problem into two subproblems by setting 
(x + -0.1428571429) equal to 1.078547777 and -1.078547777.

Subproblem 1

x + -0.1428571429 = 1.078547777 Simplifying x + -0.1428571429 = 1.078547777 Reorder the terms: -0.1428571429 + x = 1.078547777 Solving -0.1428571429 + x = 1.078547777 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 = 1.078547777 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 1.078547777 + 0.1428571429 x = 1.078547777 + 0.1428571429 Combine like terms: 1.078547777 + 0.1428571429 = 1.2214049199 x = 1.2214049199 Simplifying x = 1.2214049199

Subproblem 2

x + -0.1428571429 = -1.078547777 Simplifying x + -0.1428571429 = -1.078547777 Reorder the terms: -0.1428571429 + x = -1.078547777 Solving -0.1428571429 + x = -1.078547777 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 = -1.078547777 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -1.078547777 + 0.1428571429 x = -1.078547777 + 0.1428571429 Combine like terms: -1.078547777 + 0.1428571429 = -0.9356906341 x = -0.9356906341 Simplifying x = -0.9356906341

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2214049199, -0.9356906341}

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