2x^2+16x+5=0

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Solution for 2x^2+16x+5=0 equation:


Simplifying
2x2 + 16x + 5 = 0

Reorder the terms:
5 + 16x + 2x2 = 0

Solving
5 + 16x + 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'.
2.5 + 8x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 8x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 8x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 8x + x2 = 0 + -2.5
8x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
8x + x2 = -2.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -2.5 + 16

Reorder the terms:
16 + 8x + x2 = -2.5 + 16

Combine like terms: -2.5 + 16 = 13.5
16 + 8x + x2 = 13.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(x + 4) equal to 3.674234614 and -3.674234614.

Subproblem 1

x + 4 = 3.674234614 Simplifying x + 4 = 3.674234614 Reorder the terms: 4 + x = 3.674234614 Solving 4 + x = 3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.674234614 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.674234614 + -4 x = 3.674234614 + -4 Combine like terms: 3.674234614 + -4 = -0.325765386 x = -0.325765386 Simplifying x = -0.325765386

Subproblem 2

x + 4 = -3.674234614 Simplifying x + 4 = -3.674234614 Reorder the terms: 4 + x = -3.674234614 Solving 4 + x = -3.674234614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.674234614 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.674234614 + -4 x = -3.674234614 + -4 Combine like terms: -3.674234614 + -4 = -7.674234614 x = -7.674234614 Simplifying x = -7.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.325765386, -7.674234614}

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