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

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


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

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

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

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = 6
((7 * 7 + x * 7) + x(7 + x)) = 6
((49 + 7x) + x(7 + x)) = 6
(49 + 7x + (7 * x + x * x)) = 6
(49 + 7x + (7x + x2)) = 6

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = 6

Solving
49 + 14x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
49 + -6 + 14x + x2 = 6 + -6

Combine like terms: 49 + -6 = 43
43 + 14x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
43 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + 14x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + 14x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 14x + x2 = 0 + -43
14x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
14x + x2 = -43

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -43 + 49

Reorder the terms:
49 + 14x + x2 = -43 + 49

Combine like terms: -43 + 49 = 6
49 + 14x + x2 = 6

Factor a perfect square on the left side:
(x + 7)(x + 7) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + 7) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + 7 = 2.449489743 Simplifying x + 7 = 2.449489743 Reorder the terms: 7 + x = 2.449489743 Solving 7 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.449489743 + -7 x = 2.449489743 + -7 Combine like terms: 2.449489743 + -7 = -4.550510257 x = -4.550510257 Simplifying x = -4.550510257

Subproblem 2

x + 7 = -2.449489743 Simplifying x + 7 = -2.449489743 Reorder the terms: 7 + x = -2.449489743 Solving 7 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.449489743 + -7 x = -2.449489743 + -7 Combine like terms: -2.449489743 + -7 = -9.449489743 x = -9.449489743 Simplifying x = -9.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.550510257, -9.449489743}

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