10x+21-3=x^2

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Solution for 10x+21-3=x^2 equation: 


Simplifying
10x + 21 + -3 = x2

Reorder the terms:
21 + -3 + 10x = x2

Combine like terms: 21 + -3 = 18
18 + 10x = x2

Solving
18 + 10x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
18 + 10x + -1x2 = 0

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

Divide each side by '-1'.
-18 + -10x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -10x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -10x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -10x + x2 = 0 + 18
-10x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-10x + x2 = 18

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 = 18 + 25

Reorder the terms:
25 + -10x + x2 = 18 + 25

Combine like terms: 18 + 25 = 43
25 + -10x + x2 = 43

Factor a perfect square on the left side:
(x + -5)(x + -5) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + -5) equal to 6.557438524 and -6.557438524.


Subproblem 1
x + -5 = 6.557438524

Simplifying
x + -5 = 6.557438524

Reorder the terms:
-5 + x = 6.557438524

Solving
-5 + x = 6.557438524

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 = 6.557438524 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.557438524 + 5
x = 6.557438524 + 5

Combine like terms: 6.557438524 + 5 = 11.557438524
x = 11.557438524

Simplifying
x = 11.557438524


Subproblem 2
x + -5 = -6.557438524

Simplifying
x + -5 = -6.557438524

Reorder the terms:
-5 + x = -6.557438524

Solving
-5 + x = -6.557438524

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 = -6.557438524 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.557438524 + 5
x = -6.557438524 + 5

Combine like terms: -6.557438524 + 5 = -1.557438524
x = -1.557438524

Simplifying
x = -1.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.557438524, -1.557438524}

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