2x+x^2+1=20.25

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Solution for 2x+x^2+1=20.25 equation: 


Simplifying
2x + x2 + 1 = 20.25

Reorder the terms:
1 + 2x + x2 = 20.25

Solving
1 + 2x + x2 = 20.25

Solving for variable 'x'.

Reorder the terms:
1 + -20.25 + 2x + x2 = 20.25 + -20.25

Combine like terms: 1 + -20.25 = -19.25
-19.25 + 2x + x2 = 20.25 + -20.25

Combine like terms: 20.25 + -20.25 = 0.00
-19.25 + 2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '19.25' to each side of the equation.
-19.25 + 2x + 19.25 + x2 = 0.00 + 19.25

Reorder the terms:
-19.25 + 19.25 + 2x + x2 = 0.00 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + 2x + x2 = 0.00 + 19.25
2x + x2 = 0.00 + 19.25

Combine like terms: 0.00 + 19.25 = 19.25
2x + x2 = 19.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 19.25 + 1

Reorder the terms:
1 + 2x + x2 = 19.25 + 1

Combine like terms: 19.25 + 1 = 20.25
1 + 2x + x2 = 20.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20.25

Calculate the square root of the right side: 4.5

Break this problem into two subproblems by setting 
(x + 1) equal to 4.5 and -4.5.


Subproblem 1
x + 1 = 4.5

Simplifying
x + 1 = 4.5

Reorder the terms:
1 + x = 4.5

Solving
1 + x = 4.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = 4.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.5 + -1
x = 4.5 + -1

Combine like terms: 4.5 + -1 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + 1 = -4.5

Simplifying
x + 1 = -4.5

Reorder the terms:
1 + x = -4.5

Solving
1 + x = -4.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + x = -4.5 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.5 + -1
x = -4.5 + -1

Combine like terms: -4.5 + -1 = -5.5
x = -5.5

Simplifying
x = -5.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -5.5}

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