2x^2+32x+119=0

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Solution for 2x^2+32x+119=0 equation:


Simplifying
2x2 + 32x + 119 = 0

Reorder the terms:
119 + 32x + 2x2 = 0

Solving
119 + 32x + 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'.
59.5 + 16x + x2 = 0

Move the constant term to the right:

Add '-59.5' to each side of the equation.
59.5 + 16x + -59.5 + x2 = 0 + -59.5

Reorder the terms:
59.5 + -59.5 + 16x + x2 = 0 + -59.5

Combine like terms: 59.5 + -59.5 = 0.0
0.0 + 16x + x2 = 0 + -59.5
16x + x2 = 0 + -59.5

Combine like terms: 0 + -59.5 = -59.5
16x + x2 = -59.5

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -59.5 + 64

Reorder the terms:
64 + 16x + x2 = -59.5 + 64

Combine like terms: -59.5 + 64 = 4.5
64 + 16x + x2 = 4.5

Factor a perfect square on the left side:
(x + 8)(x + 8) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 8) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + 8 = 2.121320344 Simplifying x + 8 = 2.121320344 Reorder the terms: 8 + x = 2.121320344 Solving 8 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 2.121320344 + -8 Combine like terms: 8 + -8 = 0 0 + x = 2.121320344 + -8 x = 2.121320344 + -8 Combine like terms: 2.121320344 + -8 = -5.878679656 x = -5.878679656 Simplifying x = -5.878679656

Subproblem 2

x + 8 = -2.121320344 Simplifying x + 8 = -2.121320344 Reorder the terms: 8 + x = -2.121320344 Solving 8 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -2.121320344 + -8 Combine like terms: 8 + -8 = 0 0 + x = -2.121320344 + -8 x = -2.121320344 + -8 Combine like terms: -2.121320344 + -8 = -10.121320344 x = -10.121320344 Simplifying x = -10.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.878679656, -10.121320344}

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