(x+1)=x^2-9x+21

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Solution for (x+1)=x^2-9x+21 equation:


Simplifying
(x + 1) = x2 + -9x + 21

Reorder the terms:
(1 + x) = x2 + -9x + 21

Remove parenthesis around (1 + x)
1 + x = x2 + -9x + 21

Reorder the terms:
1 + x = 21 + -9x + x2

Solving
1 + x = 21 + -9x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -21 + x + 9x + -1x2 = 21 + -9x + x2 + -21 + 9x + -1x2

Combine like terms: 1 + -21 = -20
-20 + x + 9x + -1x2 = 21 + -9x + x2 + -21 + 9x + -1x2

Combine like terms: x + 9x = 10x
-20 + 10x + -1x2 = 21 + -9x + x2 + -21 + 9x + -1x2

Reorder the terms:
-20 + 10x + -1x2 = 21 + -21 + -9x + 9x + x2 + -1x2

Combine like terms: 21 + -21 = 0
-20 + 10x + -1x2 = 0 + -9x + 9x + x2 + -1x2
-20 + 10x + -1x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
-20 + 10x + -1x2 = 0 + x2 + -1x2
-20 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 10x + -1x2 = 0

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

Divide each side by '-1'.
20 + -10x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10x + x2 = 0 + -20
-10x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10x + x2 = -20

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -20 + 25

Reorder the terms:
25 + -10x + x2 = -20 + 25

Combine like terms: -20 + 25 = 5
25 + -10x + x2 = 5

Factor a perfect square on the left side:
(x + -5)(x + -5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -5) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -5 = 2.236067978 Simplifying x + -5 = 2.236067978 Reorder the terms: -5 + x = 2.236067978 Solving -5 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.236067978 + 5 x = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 x = 7.236067978 Simplifying x = 7.236067978

Subproblem 2

x + -5 = -2.236067978 Simplifying x + -5 = -2.236067978 Reorder the terms: -5 + x = -2.236067978 Solving -5 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.236067978 + 5 x = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 x = 2.763932022 Simplifying x = 2.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.236067978, 2.763932022}

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