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 = 27.5
25 + 10x + x2 = 27.5

Factor a perfect square on the left side:
(x + 5)(x + 5) = 27.5

Calculate the square root of the right side: 5.244044241

Break this problem into two subproblems by setting 
(x + 5) equal to 5.244044241 and -5.244044241.

Subproblem 1

x + 5 = 5.244044241 Simplifying x + 5 = 5.244044241 Reorder the terms: 5 + x = 5.244044241 Solving 5 + x = 5.244044241 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 = 5.244044241 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.244044241 + -5 x = 5.244044241 + -5 Combine like terms: 5.244044241 + -5 = 0.244044241 x = 0.244044241 Simplifying x = 0.244044241

Subproblem 2

x + 5 = -5.244044241 Simplifying x + 5 = -5.244044241 Reorder the terms: 5 + x = -5.244044241 Solving 5 + x = -5.244044241 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 = -5.244044241 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.244044241 + -5 x = -5.244044241 + -5 Combine like terms: -5.244044241 + -5 = -10.244044241 x = -10.244044241 Simplifying x = -10.244044241

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.244044241, -10.244044241}

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