.5x^2+5x-1=0

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Solution for .5x^2+5x-1=0 equation:


Simplifying
0.5x2 + 5x + -1 = 0

Reorder the terms:
-1 + 5x + 0.5x2 = 0

Solving
-1 + 5x + 0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-2 + 10x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 10x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 10x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 10x + x2 = 0 + 2
10x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
10x + x2 = 2

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 + 25

Reorder the terms:
25 + 10x + x2 = 2 + 25

Combine like terms: 2 + 25 = 27
25 + 10x + x2 = 27

Factor a perfect square on the left side:
(x + 5)(x + 5) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + 5) equal to 5.196152423 and -5.196152423.

Subproblem 1

x + 5 = 5.196152423 Simplifying x + 5 = 5.196152423 Reorder the terms: 5 + x = 5.196152423 Solving 5 + x = 5.196152423 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 = 5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.196152423 + -5 x = 5.196152423 + -5 Combine like terms: 5.196152423 + -5 = 0.196152423 x = 0.196152423 Simplifying x = 0.196152423

Subproblem 2

x + 5 = -5.196152423 Simplifying x + 5 = -5.196152423 Reorder the terms: 5 + x = -5.196152423 Solving 5 + x = -5.196152423 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 = -5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.196152423 + -5 x = -5.196152423 + -5 Combine like terms: -5.196152423 + -5 = -10.196152423 x = -10.196152423 Simplifying x = -10.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.196152423, -10.196152423}

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