2x^2-37x-34=0

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Solution for 2x^2-37x-34=0 equation:


Simplifying
2x2 + -37x + -34 = 0

Reorder the terms:
-34 + -37x + 2x2 = 0

Solving
-34 + -37x + 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'.
-17 + -18.5x + x2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -18.5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -18.5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -18.5x + x2 = 0 + 17
-18.5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-18.5x + x2 = 17

The x term is -18.5x.  Take half its coefficient (-9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
-18.5x + 85.5625 + x2 = 17 + 85.5625

Reorder the terms:
85.5625 + -18.5x + x2 = 17 + 85.5625

Combine like terms: 17 + 85.5625 = 102.5625
85.5625 + -18.5x + x2 = 102.5625

Factor a perfect square on the left side:
(x + -9.25)(x + -9.25) = 102.5625

Calculate the square root of the right side: 10.12731455

Break this problem into two subproblems by setting 
(x + -9.25) equal to 10.12731455 and -10.12731455.

Subproblem 1

x + -9.25 = 10.12731455 Simplifying x + -9.25 = 10.12731455 Reorder the terms: -9.25 + x = 10.12731455 Solving -9.25 + x = 10.12731455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = 10.12731455 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = 10.12731455 + 9.25 x = 10.12731455 + 9.25 Combine like terms: 10.12731455 + 9.25 = 19.37731455 x = 19.37731455 Simplifying x = 19.37731455

Subproblem 2

x + -9.25 = -10.12731455 Simplifying x + -9.25 = -10.12731455 Reorder the terms: -9.25 + x = -10.12731455 Solving -9.25 + x = -10.12731455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + x = -10.12731455 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + x = -10.12731455 + 9.25 x = -10.12731455 + 9.25 Combine like terms: -10.12731455 + 9.25 = -0.87731455 x = -0.87731455 Simplifying x = -0.87731455

Solution

The solution to the problem is based on the solutions from the subproblems. x = {19.37731455, -0.87731455}

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