(7x+22)(7x+22)=6

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Solution for (7x+22)(7x+22)=6 equation:


Simplifying
(7x + 22)(7x + 22) = 6

Reorder the terms:
(22 + 7x)(7x + 22) = 6

Reorder the terms:
(22 + 7x)(22 + 7x) = 6

Multiply (22 + 7x) * (22 + 7x)
(22(22 + 7x) + 7x * (22 + 7x)) = 6
((22 * 22 + 7x * 22) + 7x * (22 + 7x)) = 6
((484 + 154x) + 7x * (22 + 7x)) = 6
(484 + 154x + (22 * 7x + 7x * 7x)) = 6
(484 + 154x + (154x + 49x2)) = 6

Combine like terms: 154x + 154x = 308x
(484 + 308x + 49x2) = 6

Solving
484 + 308x + 49x2 = 6

Solving for variable 'x'.

Reorder the terms:
484 + -6 + 308x + 49x2 = 6 + -6

Combine like terms: 484 + -6 = 478
478 + 308x + 49x2 = 6 + -6

Combine like terms: 6 + -6 = 0
478 + 308x + 49x2 = 0

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

Divide each side by '49'.
9.755102041 + 6.285714286x + x2 = 0

Move the constant term to the right:

Add '-9.755102041' to each side of the equation.
9.755102041 + 6.285714286x + -9.755102041 + x2 = 0 + -9.755102041

Reorder the terms:
9.755102041 + -9.755102041 + 6.285714286x + x2 = 0 + -9.755102041

Combine like terms: 9.755102041 + -9.755102041 = 0.000000000
0.000000000 + 6.285714286x + x2 = 0 + -9.755102041
6.285714286x + x2 = 0 + -9.755102041

Combine like terms: 0 + -9.755102041 = -9.755102041
6.285714286x + x2 = -9.755102041

The x term is 6.285714286x.  Take half its coefficient (3.142857143).
Square it (9.877551021) and add it to both sides.

Add '9.877551021' to each side of the equation.
6.285714286x + 9.877551021 + x2 = -9.755102041 + 9.877551021

Reorder the terms:
9.877551021 + 6.285714286x + x2 = -9.755102041 + 9.877551021

Combine like terms: -9.755102041 + 9.877551021 = 0.12244898
9.877551021 + 6.285714286x + x2 = 0.12244898

Factor a perfect square on the left side:
(x + 3.142857143)(x + 3.142857143) = 0.12244898

Calculate the square root of the right side: 0.349927107

Break this problem into two subproblems by setting 
(x + 3.142857143) equal to 0.349927107 and -0.349927107.

Subproblem 1

x + 3.142857143 = 0.349927107 Simplifying x + 3.142857143 = 0.349927107 Reorder the terms: 3.142857143 + x = 0.349927107 Solving 3.142857143 + x = 0.349927107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.142857143' to each side of the equation. 3.142857143 + -3.142857143 + x = 0.349927107 + -3.142857143 Combine like terms: 3.142857143 + -3.142857143 = 0.000000000 0.000000000 + x = 0.349927107 + -3.142857143 x = 0.349927107 + -3.142857143 Combine like terms: 0.349927107 + -3.142857143 = -2.792930036 x = -2.792930036 Simplifying x = -2.792930036

Subproblem 2

x + 3.142857143 = -0.349927107 Simplifying x + 3.142857143 = -0.349927107 Reorder the terms: 3.142857143 + x = -0.349927107 Solving 3.142857143 + x = -0.349927107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.142857143' to each side of the equation. 3.142857143 + -3.142857143 + x = -0.349927107 + -3.142857143 Combine like terms: 3.142857143 + -3.142857143 = 0.000000000 0.000000000 + x = -0.349927107 + -3.142857143 x = -0.349927107 + -3.142857143 Combine like terms: -0.349927107 + -3.142857143 = -3.49278425 x = -3.49278425 Simplifying x = -3.49278425

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.792930036, -3.49278425}

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