2x^2+35x+120=0

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Solution for 2x^2+35x+120=0 equation:


Simplifying
2x2 + 35x + 120 = 0

Reorder the terms:
120 + 35x + 2x2 = 0

Solving
120 + 35x + 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'.
60 + 17.5x + x2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + 17.5x + -60 + x2 = 0 + -60

Reorder the terms:
60 + -60 + 17.5x + x2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 17.5x + x2 = 0 + -60
17.5x + x2 = 0 + -60

Combine like terms: 0 + -60 = -60
17.5x + x2 = -60

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = -60 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = -60 + 76.5625

Combine like terms: -60 + 76.5625 = 16.5625
76.5625 + 17.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + 8.75) equal to 4.069705149 and -4.069705149.

Subproblem 1

x + 8.75 = 4.069705149 Simplifying x + 8.75 = 4.069705149 Reorder the terms: 8.75 + x = 4.069705149 Solving 8.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 4.069705149 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 4.069705149 + -8.75 x = 4.069705149 + -8.75 Combine like terms: 4.069705149 + -8.75 = -4.680294851 x = -4.680294851 Simplifying x = -4.680294851

Subproblem 2

x + 8.75 = -4.069705149 Simplifying x + 8.75 = -4.069705149 Reorder the terms: 8.75 + x = -4.069705149 Solving 8.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -4.069705149 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -4.069705149 + -8.75 x = -4.069705149 + -8.75 Combine like terms: -4.069705149 + -8.75 = -12.819705149 x = -12.819705149 Simplifying x = -12.819705149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.680294851, -12.819705149}

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