x^2+0.5x=0.68

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Solution for x^2+0.5x=0.68 equation: 


Simplifying
x2 + 0.5x = 0.68

Reorder the terms:
0.5x + x2 = 0.68

Solving
0.5x + x2 = 0.68

Solving for variable 'x'.

Reorder the terms:
-0.68 + 0.5x + x2 = 0.68 + -0.68

Combine like terms: 0.68 + -0.68 = 0.00
-0.68 + 0.5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.68' to each side of the equation.
-0.68 + 0.5x + 0.68 + x2 = 0.00 + 0.68

Reorder the terms:
-0.68 + 0.68 + 0.5x + x2 = 0.00 + 0.68

Combine like terms: -0.68 + 0.68 = 0.00
0.00 + 0.5x + x2 = 0.00 + 0.68
0.5x + x2 = 0.00 + 0.68

Combine like terms: 0.00 + 0.68 = 0.68
0.5x + x2 = 0.68

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.68 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.68 + 0.0625

Combine like terms: 0.68 + 0.0625 = 0.7425
0.0625 + 0.5x + x2 = 0.7425

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.7425

Calculate the square root of the right side: 0.861684397

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.861684397 and -0.861684397.


Subproblem 1
x + 0.25 = 0.861684397

Simplifying
x + 0.25 = 0.861684397

Reorder the terms:
0.25 + x = 0.861684397

Solving
0.25 + x = 0.861684397

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.861684397 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.861684397 + -0.25
x = 0.861684397 + -0.25

Combine like terms: 0.861684397 + -0.25 = 0.611684397
x = 0.611684397

Simplifying
x = 0.611684397


Subproblem 2
x + 0.25 = -0.861684397

Simplifying
x + 0.25 = -0.861684397

Reorder the terms:
0.25 + x = -0.861684397

Solving
0.25 + x = -0.861684397

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.861684397 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.861684397 + -0.25
x = -0.861684397 + -0.25

Combine like terms: -0.861684397 + -0.25 = -1.111684397
x = -1.111684397

Simplifying
x = -1.111684397


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.611684397, -1.111684397}

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