6+4(4.5-x)=4+x^2

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Solution for 6+4(4.5-x)=4+x^2 equation: 


Simplifying
6 + 4(4.5 + -1x) = 4 + x2
6 + (4.5 * 4 + -1x * 4) = 4 + x2
6 + (18 + -4x) = 4 + x2

Combine like terms: 6 + 18 = 24
24 + -4x = 4 + x2

Solving
24 + -4x = 4 + x2

Solving for variable 'x'.

Reorder the terms:
24 + -4 + -4x + -1x2 = 4 + x2 + -4 + -1x2

Combine like terms: 24 + -4 = 20
20 + -4x + -1x2 = 4 + x2 + -4 + -1x2

Reorder the terms:
20 + -4x + -1x2 = 4 + -4 + x2 + -1x2

Combine like terms: 4 + -4 = 0
20 + -4x + -1x2 = 0 + x2 + -1x2
20 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-20 + 4x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 4x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 4x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 4x + x2 = 0 + 20
4x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
4x + x2 = 20

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 20 + 4

Reorder the terms:
4 + 4x + x2 = 20 + 4

Combine like terms: 20 + 4 = 24
4 + 4x + x2 = 24

Factor a perfect square on the left side:
(x + 2)(x + 2) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 2) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 2 = 4.898979486

Simplifying
x + 2 = 4.898979486

Reorder the terms:
2 + x = 4.898979486

Solving
2 + x = 4.898979486

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.898979486 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.898979486 + -2
x = 4.898979486 + -2

Combine like terms: 4.898979486 + -2 = 2.898979486
x = 2.898979486

Simplifying
x = 2.898979486


Subproblem 2
x + 2 = -4.898979486

Simplifying
x + 2 = -4.898979486

Reorder the terms:
2 + x = -4.898979486

Solving
2 + x = -4.898979486

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.898979486 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.898979486 + -2
x = -4.898979486 + -2

Combine like terms: -4.898979486 + -2 = -6.898979486
x = -6.898979486

Simplifying
x = -6.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.898979486, -6.898979486}

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