91=(x+1)(x+2)

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Solution for 91=(x+1)(x+2) equation:


Simplifying
91 = (x + 1)(x + 2)

Reorder the terms:
91 = (1 + x)(x + 2)

Reorder the terms:
91 = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
91 = (1(2 + x) + x(2 + x))
91 = ((2 * 1 + x * 1) + x(2 + x))
91 = ((2 + 1x) + x(2 + x))
91 = (2 + 1x + (2 * x + x * x))
91 = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
91 = (2 + 3x + x2)

Solving
91 = 2 + 3x + x2

Solving for variable 'x'.

Combine like terms: 91 + -2 = 89
89 + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
89 + -3x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
89 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
89 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
89 + -3x + -1x2 = 0 + x2 + -1x2
89 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
89 + -3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-89 + 3x + x2 = 0

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + 3x + 89 + x2 = 0 + 89

Reorder the terms:
-89 + 89 + 3x + x2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + 3x + x2 = 0 + 89
3x + x2 = 0 + 89

Combine like terms: 0 + 89 = 89
3x + x2 = 89

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 89 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 89 + 2.25

Combine like terms: 89 + 2.25 = 91.25
2.25 + 3x + x2 = 91.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 91.25

Calculate the square root of the right side: 9.552486587

Break this problem into two subproblems by setting 
(x + 1.5) equal to 9.552486587 and -9.552486587.

Subproblem 1

x + 1.5 = 9.552486587 Simplifying x + 1.5 = 9.552486587 Reorder the terms: 1.5 + x = 9.552486587 Solving 1.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.552486587 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.552486587 + -1.5 x = 9.552486587 + -1.5 Combine like terms: 9.552486587 + -1.5 = 8.052486587 x = 8.052486587 Simplifying x = 8.052486587

Subproblem 2

x + 1.5 = -9.552486587 Simplifying x + 1.5 = -9.552486587 Reorder the terms: 1.5 + x = -9.552486587 Solving 1.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.552486587 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.552486587 + -1.5 x = -9.552486587 + -1.5 Combine like terms: -9.552486587 + -1.5 = -11.052486587 x = -11.052486587 Simplifying x = -11.052486587

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.052486587, -11.052486587}

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