2x+2x^2+2=19

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Solution for 2x+2x^2+2=19 equation:


Simplifying
2x + 2x2 + 2 = 19

Reorder the terms:
2 + 2x + 2x2 = 19

Solving
2 + 2x + 2x2 = 19

Solving for variable 'x'.

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

Combine like terms: 2 + -19 = -17
-17 + 2x + 2x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-17 + 2x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x + x2 = 0 + 8.5
x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
x + x2 = 8.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 8.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 8.5 + 0.25

Combine like terms: 8.5 + 0.25 = 8.75
1.25 + x2 = 8.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

x + 0.5 = 2.958039892 Simplifying x + 0.5 = 2.958039892 Reorder the terms: 0.5 + x = 2.958039892 Solving 0.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.958039892 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.958039892 + -0.5 x = 2.958039892 + -0.5 Combine like terms: 2.958039892 + -0.5 = 2.458039892 x = 2.458039892 Simplifying x = 2.458039892

Subproblem 2

x + 0.5 = -2.958039892 Simplifying x + 0.5 = -2.958039892 Reorder the terms: 0.5 + x = -2.958039892 Solving 0.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.958039892 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.958039892 + -0.5 x = -2.958039892 + -0.5 Combine like terms: -2.958039892 + -0.5 = -3.458039892 x = -3.458039892 Simplifying x = -3.458039892

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.458039892, -3.458039892}

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