(x+1)(x-7)=1

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Solution for (x+1)(x-7)=1 equation:


Simplifying
(x + 1)(x + -7) = 1

Reorder the terms:
(1 + x)(x + -7) = 1

Reorder the terms:
(1 + x)(-7 + x) = 1

Multiply (1 + x) * (-7 + x)
(1(-7 + x) + x(-7 + x)) = 1
((-7 * 1 + x * 1) + x(-7 + x)) = 1
((-7 + 1x) + x(-7 + x)) = 1
(-7 + 1x + (-7 * x + x * x)) = 1
(-7 + 1x + (-7x + x2)) = 1

Combine like terms: 1x + -7x = -6x
(-7 + -6x + x2) = 1

Solving
-7 + -6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-7 + -1 + -6x + x2 = 1 + -1

Combine like terms: -7 + -1 = -8
-8 + -6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-8 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -6x + x2 = 0 + 8
-6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-6x + x2 = 8

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 = 8 + 9

Reorder the terms:
9 + -6x + x2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + -6x + x2 = 17

Factor a perfect square on the left side:
(x + -3)(x + -3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -3) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -3 = 4.123105626 Simplifying x + -3 = 4.123105626 Reorder the terms: -3 + x = 4.123105626 Solving -3 + x = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.123105626 + 3 x = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 x = 7.123105626 Simplifying x = 7.123105626

Subproblem 2

x + -3 = -4.123105626 Simplifying x + -3 = -4.123105626 Reorder the terms: -3 + x = -4.123105626 Solving -3 + x = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.123105626 + 3 x = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 x = -1.123105626 Simplifying x = -1.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.123105626, -1.123105626}

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