(x+1)(x+5)=3

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Solution for (x+1)(x+5)=3 equation:


Simplifying
(x + 1)(x + 5) = 3

Reorder the terms:
(1 + x)(x + 5) = 3

Reorder the terms:
(1 + x)(5 + x) = 3

Multiply (1 + x) * (5 + x)
(1(5 + x) + x(5 + x)) = 3
((5 * 1 + x * 1) + x(5 + x)) = 3
((5 + 1x) + x(5 + x)) = 3
(5 + 1x + (5 * x + x * x)) = 3
(5 + 1x + (5x + x2)) = 3

Combine like terms: 1x + 5x = 6x
(5 + 6x + x2) = 3

Solving
5 + 6x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
5 + -3 + 6x + x2 = 3 + -3

Combine like terms: 5 + -3 = 2
2 + 6x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
2 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6x + x2 = 0 + -2
6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
6x + x2 = -2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + 6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6x + x2 = 7

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 3) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 3 = 2.645751311 Simplifying x + 3 = 2.645751311 Reorder the terms: 3 + x = 2.645751311 Solving 3 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.645751311 + -3 x = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 x = -0.354248689 Simplifying x = -0.354248689

Subproblem 2

x + 3 = -2.645751311 Simplifying x + 3 = -2.645751311 Reorder the terms: 3 + x = -2.645751311 Solving 3 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.645751311 + -3 x = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 x = -5.645751311 Simplifying x = -5.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.354248689, -5.645751311}

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