5+2x(x-2)=19

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Solution for 5+2x(x-2)=19 equation: 


Simplifying
5 + 2x(x + -2) = 19

Reorder the terms:
5 + 2x(-2 + x) = 19
5 + (-2 * 2x + x * 2x) = 19
5 + (-4x + 2x2) = 19

Solving
5 + -4x + 2x2 = 19

Solving for variable 'x'.

Reorder the terms:
5 + -19 + -4x + 2x2 = 19 + -19

Combine like terms: 5 + -19 = -14
-14 + -4x + 2x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-14 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-7 + -2x + x2 = 0

Solving
-7 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -2x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x + x2 = 0 + 7
-2x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2x + x2 = 7

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 = 7 + 1

Reorder the terms:
1 + -2x + x2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2x + x2 = 8

Factor a perfect square on the left side:
(x + -1)(x + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -1) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -1 = 2.828427125

Simplifying
x + -1 = 2.828427125

Reorder the terms:
-1 + x = 2.828427125

Solving
-1 + x = 2.828427125

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 = 2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.828427125 + 1
x = 2.828427125 + 1

Combine like terms: 2.828427125 + 1 = 3.828427125
x = 3.828427125

Simplifying
x = 3.828427125


Subproblem 2
x + -1 = -2.828427125

Simplifying
x + -1 = -2.828427125

Reorder the terms:
-1 + x = -2.828427125

Solving
-1 + x = -2.828427125

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 = -2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.828427125 + 1
x = -2.828427125 + 1

Combine like terms: -2.828427125 + 1 = -1.828427125
x = -1.828427125

Simplifying
x = -1.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.828427125, -1.828427125}
Solution
x = {3.828427125, -1.828427125}

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