2x^2+8x+1=

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Solution for 2x^2+8x+1= equation:


Simplifying
2x2 + 8x + 1 = 0

Reorder the terms:
1 + 8x + 2x2 = 0

Solving
1 + 8x + 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'.
0.5 + 4x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4x + x2 = 0 + -0.5
4x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4x + x2 = -0.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -0.5 + 4

Reorder the terms:
4 + 4x + x2 = -0.5 + 4

Combine like terms: -0.5 + 4 = 3.5
4 + 4x + x2 = 3.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(x + 2) equal to 1.870828693 and -1.870828693.

Subproblem 1

x + 2 = 1.870828693 Simplifying x + 2 = 1.870828693 Reorder the terms: 2 + x = 1.870828693 Solving 2 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.870828693 + -2 x = 1.870828693 + -2 Combine like terms: 1.870828693 + -2 = -0.129171307 x = -0.129171307 Simplifying x = -0.129171307

Subproblem 2

x + 2 = -1.870828693 Simplifying x + 2 = -1.870828693 Reorder the terms: 2 + x = -1.870828693 Solving 2 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.870828693 + -2 x = -1.870828693 + -2 Combine like terms: -1.870828693 + -2 = -3.870828693 x = -3.870828693 Simplifying x = -3.870828693

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.129171307, -3.870828693}

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