2x^2+20x+5=0

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


Simplifying
2x2 + 20x + 5 = 0

Reorder the terms:
5 + 20x + 2x2 = 0

Solving
5 + 20x + 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 + 10x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 10x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 10x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 10x + x2 = 0 + -2.5
10x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
10x + x2 = -2.5

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -2.5 + 25

Reorder the terms:
25 + 10x + x2 = -2.5 + 25

Combine like terms: -2.5 + 25 = 22.5
25 + 10x + x2 = 22.5

Factor a perfect square on the left side:
(x + 5)(x + 5) = 22.5

Calculate the square root of the right side: 4.74341649

Break this problem into two subproblems by setting 
(x + 5) equal to 4.74341649 and -4.74341649.

Subproblem 1

x + 5 = 4.74341649 Simplifying x + 5 = 4.74341649 Reorder the terms: 5 + x = 4.74341649 Solving 5 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.74341649 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.74341649 + -5 x = 4.74341649 + -5 Combine like terms: 4.74341649 + -5 = -0.25658351 x = -0.25658351 Simplifying x = -0.25658351

Subproblem 2

x + 5 = -4.74341649 Simplifying x + 5 = -4.74341649 Reorder the terms: 5 + x = -4.74341649 Solving 5 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.74341649 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.74341649 + -5 x = -4.74341649 + -5 Combine like terms: -4.74341649 + -5 = -9.74341649 x = -9.74341649 Simplifying x = -9.74341649

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.25658351, -9.74341649}

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