2x^2+2x-39=0

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Solution for 2x^2+2x-39=0 equation:


Simplifying
2x2 + 2x + -39 = 0

Reorder the terms:
-39 + 2x + 2x2 = 0

Solving
-39 + 2x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-19.5 + x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + x + x2 = 0 + 19.5
x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
x + x2 = 19.5

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 = 19.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 19.5 + 0.25

Combine like terms: 19.5 + 0.25 = 19.75
1.25 + x2 = 19.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.444097209 and -4.444097209.

Subproblem 1

x + 0.5 = 4.444097209 Simplifying x + 0.5 = 4.444097209 Reorder the terms: 0.5 + x = 4.444097209 Solving 0.5 + x = 4.444097209 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 = 4.444097209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.444097209 + -0.5 x = 4.444097209 + -0.5 Combine like terms: 4.444097209 + -0.5 = 3.944097209 x = 3.944097209 Simplifying x = 3.944097209

Subproblem 2

x + 0.5 = -4.444097209 Simplifying x + 0.5 = -4.444097209 Reorder the terms: 0.5 + x = -4.444097209 Solving 0.5 + x = -4.444097209 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 = -4.444097209 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.444097209 + -0.5 x = -4.444097209 + -0.5 Combine like terms: -4.444097209 + -0.5 = -4.944097209 x = -4.944097209 Simplifying x = -4.944097209

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.944097209, -4.944097209}

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