2x^2+3x-13=0

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Solution for 2x^2+3x-13=0 equation: 


Simplifying
2x2 + 3x + -13 = 0

Reorder the terms:
-13 + 3x + 2x2 = 0

Solving
-13 + 3x + 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'.
-6.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 1.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 1.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 1.5x + x2 = 0 + 6.5
1.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
1.5x + x2 = 6.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 6.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 6.5 + 0.5625

Combine like terms: 6.5 + 0.5625 = 7.0625
0.5625 + 1.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.657536453 and -2.657536453.


Subproblem 1
x + 0.75 = 2.657536453

Simplifying
x + 0.75 = 2.657536453

Reorder the terms:
0.75 + x = 2.657536453

Solving
0.75 + x = 2.657536453

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.657536453 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.657536453 + -0.75
x = 2.657536453 + -0.75

Combine like terms: 2.657536453 + -0.75 = 1.907536453
x = 1.907536453

Simplifying
x = 1.907536453


Subproblem 2
x + 0.75 = -2.657536453

Simplifying
x + 0.75 = -2.657536453

Reorder the terms:
0.75 + x = -2.657536453

Solving
0.75 + x = -2.657536453

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.657536453 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.657536453 + -0.75
x = -2.657536453 + -0.75

Combine like terms: -2.657536453 + -0.75 = -3.407536453
x = -3.407536453

Simplifying
x = -3.407536453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.907536453, -3.407536453}

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