2x^2+5x-38=0

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Solution for 2x^2+5x-38=0 equation:


Simplifying
2x2 + 5x + -38 = 0

Reorder the terms:
-38 + 5x + 2x2 = 0

Solving
-38 + 5x + 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 + 2.5x + x2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2.5x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 2.5x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2.5x + x2 = 0 + 19
2.5x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
2.5x + x2 = 19

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 19 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 19 + 1.5625

Combine like terms: 19 + 1.5625 = 20.5625
1.5625 + 2.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + 1.25) equal to 4.534589287 and -4.534589287.

Subproblem 1

x + 1.25 = 4.534589287 Simplifying x + 1.25 = 4.534589287 Reorder the terms: 1.25 + x = 4.534589287 Solving 1.25 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 4.534589287 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 4.534589287 + -1.25 x = 4.534589287 + -1.25 Combine like terms: 4.534589287 + -1.25 = 3.284589287 x = 3.284589287 Simplifying x = 3.284589287

Subproblem 2

x + 1.25 = -4.534589287 Simplifying x + 1.25 = -4.534589287 Reorder the terms: 1.25 + x = -4.534589287 Solving 1.25 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -4.534589287 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -4.534589287 + -1.25 x = -4.534589287 + -1.25 Combine like terms: -4.534589287 + -1.25 = -5.784589287 x = -5.784589287 Simplifying x = -5.784589287

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.284589287, -5.784589287}

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