(x+7)(x+5)=16

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Solution for (x+7)(x+5)=16 equation:


Simplifying
(x + 7)(x + 5) = 16

Reorder the terms:
(7 + x)(x + 5) = 16

Reorder the terms:
(7 + x)(5 + x) = 16

Multiply (7 + x) * (5 + x)
(7(5 + x) + x(5 + x)) = 16
((5 * 7 + x * 7) + x(5 + x)) = 16
((35 + 7x) + x(5 + x)) = 16
(35 + 7x + (5 * x + x * x)) = 16
(35 + 7x + (5x + x2)) = 16

Combine like terms: 7x + 5x = 12x
(35 + 12x + x2) = 16

Solving
35 + 12x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
35 + -16 + 12x + x2 = 16 + -16

Combine like terms: 35 + -16 = 19
19 + 12x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
19 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + 12x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + 12x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 12x + x2 = 0 + -19
12x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
12x + x2 = -19

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -19 + 36

Reorder the terms:
36 + 12x + x2 = -19 + 36

Combine like terms: -19 + 36 = 17
36 + 12x + x2 = 17

Factor a perfect square on the left side:
(x + 6)(x + 6) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + 6) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + 6 = 4.123105626 Simplifying x + 6 = 4.123105626 Reorder the terms: 6 + x = 4.123105626 Solving 6 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.123105626 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.123105626 + -6 x = 4.123105626 + -6 Combine like terms: 4.123105626 + -6 = -1.876894374 x = -1.876894374 Simplifying x = -1.876894374

Subproblem 2

x + 6 = -4.123105626 Simplifying x + 6 = -4.123105626 Reorder the terms: 6 + x = -4.123105626 Solving 6 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.123105626 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.123105626 + -6 x = -4.123105626 + -6 Combine like terms: -4.123105626 + -6 = -10.123105626 x = -10.123105626 Simplifying x = -10.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.876894374, -10.123105626}

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