x(x-15.50)=47.5

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Solution for x(x-15.50)=47.5 equation: 


Simplifying
x(x + -15.50) = 47.5

Reorder the terms:
x(-15.50 + x) = 47.5
(-15.50 * x + x * x) = 47.5
(-15.50x + x2) = 47.5

Solving
-15.50x + x2 = 47.5

Solving for variable 'x'.

Reorder the terms:
-47.5 + -15.50x + x2 = 47.5 + -47.5

Combine like terms: 47.5 + -47.5 = 0.0
-47.5 + -15.50x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '47.5' to each side of the equation.
-47.5 + -15.50x + 47.5 + x2 = 0.0 + 47.5

Reorder the terms:
-47.5 + 47.5 + -15.50x + x2 = 0.0 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + -15.50x + x2 = 0.0 + 47.5
-15.50x + x2 = 0.0 + 47.5

Combine like terms: 0.0 + 47.5 = 47.5
-15.50x + x2 = 47.5

The x term is -15.50x.  Take half its coefficient (-7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
-15.50x + 60.0625 + x2 = 47.5 + 60.0625

Reorder the terms:
60.0625 + -15.50x + x2 = 47.5 + 60.0625

Combine like terms: 47.5 + 60.0625 = 107.5625
60.0625 + -15.50x + x2 = 107.5625

Factor a perfect square on the left side:
(x + -7.75)(x + -7.75) = 107.5625

Calculate the square root of the right side: 10.371234256

Break this problem into two subproblems by setting 
(x + -7.75) equal to 10.371234256 and -10.371234256.


Subproblem 1
x + -7.75 = 10.371234256

Simplifying
x + -7.75 = 10.371234256

Reorder the terms:
-7.75 + x = 10.371234256

Solving
-7.75 + x = 10.371234256

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = 10.371234256 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = 10.371234256 + 7.75
x = 10.371234256 + 7.75

Combine like terms: 10.371234256 + 7.75 = 18.121234256
x = 18.121234256

Simplifying
x = 18.121234256


Subproblem 2
x + -7.75 = -10.371234256

Simplifying
x + -7.75 = -10.371234256

Reorder the terms:
-7.75 + x = -10.371234256

Solving
-7.75 + x = -10.371234256

Solving for variable 'x'.

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

Add '7.75' to each side of the equation.
-7.75 + 7.75 + x = -10.371234256 + 7.75

Combine like terms: -7.75 + 7.75 = 0.00
0.00 + x = -10.371234256 + 7.75
x = -10.371234256 + 7.75

Combine like terms: -10.371234256 + 7.75 = -2.621234256
x = -2.621234256

Simplifying
x = -2.621234256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.121234256, -2.621234256}

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