7x^2=16+x

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Solution for 7x^2=16+x equation:


Simplifying
7x2 = 16 + x

Solving
7x2 = 16 + x

Solving for variable 'x'.

Reorder the terms:
-16 + -1x + 7x2 = 16 + x + -16 + -1x

Reorder the terms:
-16 + -1x + 7x2 = 16 + -16 + x + -1x

Combine like terms: 16 + -16 = 0
-16 + -1x + 7x2 = 0 + x + -1x
-16 + -1x + 7x2 = x + -1x

Combine like terms: x + -1x = 0
-16 + -1x + 7x2 = 0

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

Divide each side by '7'.
-2.285714286 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '2.285714286' to each side of the equation.
-2.285714286 + -0.1428571429x + 2.285714286 + x2 = 0 + 2.285714286

Reorder the terms:
-2.285714286 + 2.285714286 + -0.1428571429x + x2 = 0 + 2.285714286

Combine like terms: -2.285714286 + 2.285714286 = 0.000000000
0.000000000 + -0.1428571429x + x2 = 0 + 2.285714286
-0.1428571429x + x2 = 0 + 2.285714286

Combine like terms: 0 + 2.285714286 = 2.285714286
-0.1428571429x + x2 = 2.285714286

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 = 2.285714286 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 2.285714286 + 0.005102040819

Combine like terms: 2.285714286 + 0.005102040819 = 2.290816326819
0.005102040819 + -0.1428571429x + x2 = 2.290816326819

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 2.290816326819

Calculate the square root of the right side: 1.513544293

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 1.513544293 and -1.513544293.

Subproblem 1

x + -0.07142857145 = 1.513544293 Simplifying x + -0.07142857145 = 1.513544293 Reorder the terms: -0.07142857145 + x = 1.513544293 Solving -0.07142857145 + x = 1.513544293 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 = 1.513544293 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 1.513544293 + 0.07142857145 x = 1.513544293 + 0.07142857145 Combine like terms: 1.513544293 + 0.07142857145 = 1.58497286445 x = 1.58497286445 Simplifying x = 1.58497286445

Subproblem 2

x + -0.07142857145 = -1.513544293 Simplifying x + -0.07142857145 = -1.513544293 Reorder the terms: -0.07142857145 + x = -1.513544293 Solving -0.07142857145 + x = -1.513544293 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 = -1.513544293 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -1.513544293 + 0.07142857145 x = -1.513544293 + 0.07142857145 Combine like terms: -1.513544293 + 0.07142857145 = -1.44211572155 x = -1.44211572155 Simplifying x = -1.44211572155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.58497286445, -1.44211572155}

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