x*(x+0.5)=5.67

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Solution for x*(x+0.5)=5.67 equation: 


Simplifying
x(x + 0.5) = 5.67

Reorder the terms:
x(0.5 + x) = 5.67
(0.5 * x + x * x) = 5.67
(0.5x + x2) = 5.67

Solving
0.5x + x2 = 5.67

Solving for variable 'x'.

Reorder the terms:
-5.67 + 0.5x + x2 = 5.67 + -5.67

Combine like terms: 5.67 + -5.67 = 0.00
-5.67 + 0.5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '5.67' to each side of the equation.
-5.67 + 0.5x + 5.67 + x2 = 0.00 + 5.67

Reorder the terms:
-5.67 + 5.67 + 0.5x + x2 = 0.00 + 5.67

Combine like terms: -5.67 + 5.67 = 0.00
0.00 + 0.5x + x2 = 0.00 + 5.67
0.5x + x2 = 0.00 + 5.67

Combine like terms: 0.00 + 5.67 = 5.67
0.5x + x2 = 5.67

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 = 5.67 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 5.67 + 0.0625

Combine like terms: 5.67 + 0.0625 = 5.7325
0.0625 + 0.5x + x2 = 5.7325

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 5.7325

Calculate the square root of the right side: 2.394263979

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.394263979 and -2.394263979.


Subproblem 1
x + 0.25 = 2.394263979

Simplifying
x + 0.25 = 2.394263979

Reorder the terms:
0.25 + x = 2.394263979

Solving
0.25 + x = 2.394263979

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 = 2.394263979 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 2.394263979 + -0.25
x = 2.394263979 + -0.25

Combine like terms: 2.394263979 + -0.25 = 2.144263979
x = 2.144263979

Simplifying
x = 2.144263979


Subproblem 2
x + 0.25 = -2.394263979

Simplifying
x + 0.25 = -2.394263979

Reorder the terms:
0.25 + x = -2.394263979

Solving
0.25 + x = -2.394263979

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 = -2.394263979 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -2.394263979 + -0.25
x = -2.394263979 + -0.25

Combine like terms: -2.394263979 + -0.25 = -2.644263979
x = -2.644263979

Simplifying
x = -2.644263979


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.144263979, -2.644263979}

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