5x^2+16x+2=0

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


Simplifying
5x2 + 16x + 2 = 0

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

Solving
2 + 16x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + 3.2x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 3.2x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 3.2x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 3.2x + x2 = 0 + -0.4
3.2x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
3.2x + x2 = -0.4

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = -0.4 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = -0.4 + 2.56

Combine like terms: -0.4 + 2.56 = 2.16
2.56 + 3.2x + x2 = 2.16

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 2.16

Calculate the square root of the right side: 1.469693846

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.469693846 and -1.469693846.

Subproblem 1

x + 1.6 = 1.469693846 Simplifying x + 1.6 = 1.469693846 Reorder the terms: 1.6 + x = 1.469693846 Solving 1.6 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.469693846 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.469693846 + -1.6 x = 1.469693846 + -1.6 Combine like terms: 1.469693846 + -1.6 = -0.130306154 x = -0.130306154 Simplifying x = -0.130306154

Subproblem 2

x + 1.6 = -1.469693846 Simplifying x + 1.6 = -1.469693846 Reorder the terms: 1.6 + x = -1.469693846 Solving 1.6 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.469693846 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.469693846 + -1.6 x = -1.469693846 + -1.6 Combine like terms: -1.469693846 + -1.6 = -3.069693846 x = -3.069693846 Simplifying x = -3.069693846

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.130306154, -3.069693846}

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