5x^2+20x+8=0

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Solution for 5x^2+20x+8=0 equation:


Simplifying
5x2 + 20x + 8 = 0

Reorder the terms:
8 + 20x + 5x2 = 0

Solving
8 + 20x + 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'.
1.6 + 4x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 4x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 4x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 4x + x2 = 0 + -1.6
4x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
4x + x2 = -1.6

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 = -1.6 + 4

Reorder the terms:
4 + 4x + x2 = -1.6 + 4

Combine like terms: -1.6 + 4 = 2.4
4 + 4x + x2 = 2.4

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2.4

Calculate the square root of the right side: 1.549193338

Break this problem into two subproblems by setting 
(x + 2) equal to 1.549193338 and -1.549193338.

Subproblem 1

x + 2 = 1.549193338 Simplifying x + 2 = 1.549193338 Reorder the terms: 2 + x = 1.549193338 Solving 2 + x = 1.549193338 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 = 1.549193338 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.549193338 + -2 x = 1.549193338 + -2 Combine like terms: 1.549193338 + -2 = -0.450806662 x = -0.450806662 Simplifying x = -0.450806662

Subproblem 2

x + 2 = -1.549193338 Simplifying x + 2 = -1.549193338 Reorder the terms: 2 + x = -1.549193338 Solving 2 + x = -1.549193338 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 = -1.549193338 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.549193338 + -2 x = -1.549193338 + -2 Combine like terms: -1.549193338 + -2 = -3.549193338 x = -3.549193338 Simplifying x = -3.549193338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.450806662, -3.549193338}

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