(6+x)(8+x)=96

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Solution for (6+x)(8+x)=96 equation:


Simplifying
(6 + x)(8 + x) = 96

Multiply (6 + x) * (8 + x)
(6(8 + x) + x(8 + x)) = 96
((8 * 6 + x * 6) + x(8 + x)) = 96
((48 + 6x) + x(8 + x)) = 96
(48 + 6x + (8 * x + x * x)) = 96
(48 + 6x + (8x + x2)) = 96

Combine like terms: 6x + 8x = 14x
(48 + 14x + x2) = 96

Solving
48 + 14x + x2 = 96

Solving for variable 'x'.

Reorder the terms:
48 + -96 + 14x + x2 = 96 + -96

Combine like terms: 48 + -96 = -48
-48 + 14x + x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-48 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 14x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 14x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 14x + x2 = 0 + 48
14x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
14x + x2 = 48

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 = 48 + 49

Reorder the terms:
49 + 14x + x2 = 48 + 49

Combine like terms: 48 + 49 = 97
49 + 14x + x2 = 97

Factor a perfect square on the left side:
(x + 7)(x + 7) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 7) equal to 9.848857802 and -9.848857802.

Subproblem 1

x + 7 = 9.848857802 Simplifying x + 7 = 9.848857802 Reorder the terms: 7 + x = 9.848857802 Solving 7 + x = 9.848857802 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 = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.848857802 + -7 x = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 x = 2.848857802 Simplifying x = 2.848857802

Subproblem 2

x + 7 = -9.848857802 Simplifying x + 7 = -9.848857802 Reorder the terms: 7 + x = -9.848857802 Solving 7 + x = -9.848857802 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 = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.848857802 + -7 x = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 x = -16.848857802 Simplifying x = -16.848857802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.848857802, -16.848857802}

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