2x^2+41x+37=0

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Solution for 2x^2+41x+37=0 equation:


Simplifying
2x2 + 41x + 37 = 0

Reorder the terms:
37 + 41x + 2x2 = 0

Solving
37 + 41x + 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'.
18.5 + 20.5x + x2 = 0

Move the constant term to the right:

Add '-18.5' to each side of the equation.
18.5 + 20.5x + -18.5 + x2 = 0 + -18.5

Reorder the terms:
18.5 + -18.5 + 20.5x + x2 = 0 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + 20.5x + x2 = 0 + -18.5
20.5x + x2 = 0 + -18.5

Combine like terms: 0 + -18.5 = -18.5
20.5x + x2 = -18.5

The x term is 20.5x.  Take half its coefficient (10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
20.5x + 105.0625 + x2 = -18.5 + 105.0625

Reorder the terms:
105.0625 + 20.5x + x2 = -18.5 + 105.0625

Combine like terms: -18.5 + 105.0625 = 86.5625
105.0625 + 20.5x + x2 = 86.5625

Factor a perfect square on the left side:
(x + 10.25)(x + 10.25) = 86.5625

Calculate the square root of the right side: 9.303897033

Break this problem into two subproblems by setting 
(x + 10.25) equal to 9.303897033 and -9.303897033.

Subproblem 1

x + 10.25 = 9.303897033 Simplifying x + 10.25 = 9.303897033 Reorder the terms: 10.25 + x = 9.303897033 Solving 10.25 + x = 9.303897033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = 9.303897033 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = 9.303897033 + -10.25 x = 9.303897033 + -10.25 Combine like terms: 9.303897033 + -10.25 = -0.946102967 x = -0.946102967 Simplifying x = -0.946102967

Subproblem 2

x + 10.25 = -9.303897033 Simplifying x + 10.25 = -9.303897033 Reorder the terms: 10.25 + x = -9.303897033 Solving 10.25 + x = -9.303897033 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = -9.303897033 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = -9.303897033 + -10.25 x = -9.303897033 + -10.25 Combine like terms: -9.303897033 + -10.25 = -19.553897033 x = -19.553897033 Simplifying x = -19.553897033

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.946102967, -19.553897033}

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