5x^2+x-.5=0

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


Simplifying
5x2 + x + -0.5 = 0

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

Solving
-0.5 + x + 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'.
-0.1 + 0.2x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.2x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.2x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.2x + x2 = 0 + 0.1
0.2x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
0.2x + x2 = 0.1

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2x + 0.25 + x2 = 0.1 + 0.25

Reorder the terms:
0.25 + 0.2x + x2 = 0.1 + 0.25

Combine like terms: 0.1 + 0.25 = 0.35
0.25 + 0.2x + x2 = 0.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.591607978 and -0.591607978.

Subproblem 1

x + 0.5 = 0.591607978 Simplifying x + 0.5 = 0.591607978 Reorder the terms: 0.5 + x = 0.591607978 Solving 0.5 + x = 0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.591607978 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.591607978 + -0.5 x = 0.591607978 + -0.5 Combine like terms: 0.591607978 + -0.5 = 0.091607978 x = 0.091607978 Simplifying x = 0.091607978

Subproblem 2

x + 0.5 = -0.591607978 Simplifying x + 0.5 = -0.591607978 Reorder the terms: 0.5 + x = -0.591607978 Solving 0.5 + x = -0.591607978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.591607978 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.591607978 + -0.5 x = -0.591607978 + -0.5 Combine like terms: -0.591607978 + -0.5 = -1.091607978 x = -1.091607978 Simplifying x = -1.091607978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.091607978, -1.091607978}

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