x(x+0.5)=150

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Solution for x(x+0.5)=150 equation: 


Simplifying
x(x + 0.5) = 150

Reorder the terms:
x(0.5 + x) = 150
(0.5 * x + x * x) = 150
(0.5x + x2) = 150

Solving
0.5x + x2 = 150

Solving for variable 'x'.

Reorder the terms:
-150 + 0.5x + x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + 0.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '150' to each side of the equation.
-150 + 0.5x + 150 + x2 = 0 + 150

Reorder the terms:
-150 + 150 + 0.5x + x2 = 0 + 150

Combine like terms: -150 + 150 = 0
0 + 0.5x + x2 = 0 + 150
0.5x + x2 = 0 + 150

Combine like terms: 0 + 150 = 150
0.5x + x2 = 150

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 = 150 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 150 + 0.0625

Combine like terms: 150 + 0.0625 = 150.0625
0.0625 + 0.5x + x2 = 150.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 150.0625

Calculate the square root of the right side: 12.25

Break this problem into two subproblems by setting 
(x + 0.25) equal to 12.25 and -12.25.


Subproblem 1
x + 0.25 = 12.25

Simplifying
x + 0.25 = 12.25

Reorder the terms:
0.25 + x = 12.25

Solving
0.25 + x = 12.25

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 = 12.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 12.25 + -0.25
x = 12.25 + -0.25

Combine like terms: 12.25 + -0.25 = 12
x = 12

Simplifying
x = 12


Subproblem 2
x + 0.25 = -12.25

Simplifying
x + 0.25 = -12.25

Reorder the terms:
0.25 + x = -12.25

Solving
0.25 + x = -12.25

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 = -12.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -12.25 + -0.25
x = -12.25 + -0.25

Combine like terms: -12.25 + -0.25 = -12.5
x = -12.5

Simplifying
x = -12.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, -12.5}

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