2x^2-5x-39=0

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Solution for 2x^2-5x-39=0 equation:


Simplifying
2x2 + -5x + -39 = 0

Reorder the terms:
-39 + -5x + 2x2 = 0

Solving
-39 + -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'.
-19.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + -2.5x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + -2.5x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + -2.5x + x2 = 0 + 19.5
-2.5x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
-2.5x + x2 = 19.5

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 = 19.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 19.5 + 1.5625

Combine like terms: 19.5 + 1.5625 = 21.0625
1.5625 + -2.5x + x2 = 21.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(x + -1.25) equal to 4.589389938 and -4.589389938.

Subproblem 1

x + -1.25 = 4.589389938 Simplifying x + -1.25 = 4.589389938 Reorder the terms: -1.25 + x = 4.589389938 Solving -1.25 + x = 4.589389938 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 = 4.589389938 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.589389938 + 1.25 x = 4.589389938 + 1.25 Combine like terms: 4.589389938 + 1.25 = 5.839389938 x = 5.839389938 Simplifying x = 5.839389938

Subproblem 2

x + -1.25 = -4.589389938 Simplifying x + -1.25 = -4.589389938 Reorder the terms: -1.25 + x = -4.589389938 Solving -1.25 + x = -4.589389938 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 = -4.589389938 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.589389938 + 1.25 x = -4.589389938 + 1.25 Combine like terms: -4.589389938 + 1.25 = -3.339389938 x = -3.339389938 Simplifying x = -3.339389938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.839389938, -3.339389938}

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