(11x+7)(11x+7)=105

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Solution for (11x+7)(11x+7)=105 equation:


Simplifying
(11x + 7)(11x + 7) = 105

Reorder the terms:
(7 + 11x)(11x + 7) = 105

Reorder the terms:
(7 + 11x)(7 + 11x) = 105

Multiply (7 + 11x) * (7 + 11x)
(7(7 + 11x) + 11x * (7 + 11x)) = 105
((7 * 7 + 11x * 7) + 11x * (7 + 11x)) = 105
((49 + 77x) + 11x * (7 + 11x)) = 105
(49 + 77x + (7 * 11x + 11x * 11x)) = 105
(49 + 77x + (77x + 121x2)) = 105

Combine like terms: 77x + 77x = 154x
(49 + 154x + 121x2) = 105

Solving
49 + 154x + 121x2 = 105

Solving for variable 'x'.

Reorder the terms:
49 + -105 + 154x + 121x2 = 105 + -105

Combine like terms: 49 + -105 = -56
-56 + 154x + 121x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-56 + 154x + 121x2 = 0

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

Divide each side by '121'.
-0.4628099174 + 1.272727273x + x2 = 0

Move the constant term to the right:

Add '0.4628099174' to each side of the equation.
-0.4628099174 + 1.272727273x + 0.4628099174 + x2 = 0 + 0.4628099174

Reorder the terms:
-0.4628099174 + 0.4628099174 + 1.272727273x + x2 = 0 + 0.4628099174

Combine like terms: -0.4628099174 + 0.4628099174 = 0.0000000000
0.0000000000 + 1.272727273x + x2 = 0 + 0.4628099174
1.272727273x + x2 = 0 + 0.4628099174

Combine like terms: 0 + 0.4628099174 = 0.4628099174
1.272727273x + x2 = 0.4628099174

The x term is 1.272727273x.  Take half its coefficient (0.6363636365).
Square it (0.4049586779) and add it to both sides.

Add '0.4049586779' to each side of the equation.
1.272727273x + 0.4049586779 + x2 = 0.4628099174 + 0.4049586779

Reorder the terms:
0.4049586779 + 1.272727273x + x2 = 0.4628099174 + 0.4049586779

Combine like terms: 0.4628099174 + 0.4049586779 = 0.8677685953
0.4049586779 + 1.272727273x + x2 = 0.8677685953

Factor a perfect square on the left side:
(x + 0.6363636365)(x + 0.6363636365) = 0.8677685953

Calculate the square root of the right side: 0.931540979

Break this problem into two subproblems by setting 
(x + 0.6363636365) equal to 0.931540979 and -0.931540979.

Subproblem 1

x + 0.6363636365 = 0.931540979 Simplifying x + 0.6363636365 = 0.931540979 Reorder the terms: 0.6363636365 + x = 0.931540979 Solving 0.6363636365 + x = 0.931540979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = 0.931540979 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = 0.931540979 + -0.6363636365 x = 0.931540979 + -0.6363636365 Combine like terms: 0.931540979 + -0.6363636365 = 0.2951773425 x = 0.2951773425 Simplifying x = 0.2951773425

Subproblem 2

x + 0.6363636365 = -0.931540979 Simplifying x + 0.6363636365 = -0.931540979 Reorder the terms: 0.6363636365 + x = -0.931540979 Solving 0.6363636365 + x = -0.931540979 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6363636365' to each side of the equation. 0.6363636365 + -0.6363636365 + x = -0.931540979 + -0.6363636365 Combine like terms: 0.6363636365 + -0.6363636365 = 0.0000000000 0.0000000000 + x = -0.931540979 + -0.6363636365 x = -0.931540979 + -0.6363636365 Combine like terms: -0.931540979 + -0.6363636365 = -1.5679046155 x = -1.5679046155 Simplifying x = -1.5679046155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2951773425, -1.5679046155}

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