x^2+21x=9.74

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Solution for x^2+21x=9.74 equation: 


Simplifying
x2 + 21x = 9.74

Reorder the terms:
21x + x2 = 9.74

Solving
21x + x2 = 9.74

Solving for variable 'x'.

Reorder the terms:
-9.74 + 21x + x2 = 9.74 + -9.74

Combine like terms: 9.74 + -9.74 = 0.00
-9.74 + 21x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '9.74' to each side of the equation.
-9.74 + 21x + 9.74 + x2 = 0.00 + 9.74

Reorder the terms:
-9.74 + 9.74 + 21x + x2 = 0.00 + 9.74

Combine like terms: -9.74 + 9.74 = 0.00
0.00 + 21x + x2 = 0.00 + 9.74
21x + x2 = 0.00 + 9.74

Combine like terms: 0.00 + 9.74 = 9.74
21x + x2 = 9.74

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 9.74 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 9.74 + 110.25

Combine like terms: 9.74 + 110.25 = 119.99
110.25 + 21x + x2 = 119.99

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 119.99

Calculate the square root of the right side: 10.953994705

Break this problem into two subproblems by setting 
(x + 10.5) equal to 10.953994705 and -10.953994705.


Subproblem 1
x + 10.5 = 10.953994705

Simplifying
x + 10.5 = 10.953994705

Reorder the terms:
10.5 + x = 10.953994705

Solving
10.5 + x = 10.953994705

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 10.953994705 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 10.953994705 + -10.5
x = 10.953994705 + -10.5

Combine like terms: 10.953994705 + -10.5 = 0.453994705
x = 0.453994705

Simplifying
x = 0.453994705


Subproblem 2
x + 10.5 = -10.953994705

Simplifying
x + 10.5 = -10.953994705

Reorder the terms:
10.5 + x = -10.953994705

Solving
10.5 + x = -10.953994705

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -10.953994705 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -10.953994705 + -10.5
x = -10.953994705 + -10.5

Combine like terms: -10.953994705 + -10.5 = -21.453994705
x = -21.453994705

Simplifying
x = -21.453994705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.453994705, -21.453994705}

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