2x^2+8x+3=

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Solution for 2x^2+8x+3= equation:


Simplifying
2x2 + 8x + 3 = 0

Reorder the terms:
3 + 8x + 2x2 = 0

Solving
3 + 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'.
1.5 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 4x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 4x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 4x + x2 = 0 + -1.5
4x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
4x + x2 = -1.5

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 = -1.5 + 4

Reorder the terms:
4 + 4x + x2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + 4x + x2 = 2.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 2) equal to 1.58113883 and -1.58113883.

Subproblem 1

x + 2 = 1.58113883 Simplifying x + 2 = 1.58113883 Reorder the terms: 2 + x = 1.58113883 Solving 2 + x = 1.58113883 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 = 1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.58113883 + -2 x = 1.58113883 + -2 Combine like terms: 1.58113883 + -2 = -0.41886117 x = -0.41886117 Simplifying x = -0.41886117

Subproblem 2

x + 2 = -1.58113883 Simplifying x + 2 = -1.58113883 Reorder the terms: 2 + x = -1.58113883 Solving 2 + x = -1.58113883 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 = -1.58113883 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.58113883 + -2 x = -1.58113883 + -2 Combine like terms: -1.58113883 + -2 = -3.58113883 x = -3.58113883 Simplifying x = -3.58113883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.41886117, -3.58113883}

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