x(x-3)=10.71

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Solution for x(x-3)=10.71 equation: 


Simplifying
x(x + -3) = 10.71

Reorder the terms:
x(-3 + x) = 10.71
(-3 * x + x * x) = 10.71
(-3x + x2) = 10.71

Solving
-3x + x2 = 10.71

Solving for variable 'x'.

Reorder the terms:
-10.71 + -3x + x2 = 10.71 + -10.71

Combine like terms: 10.71 + -10.71 = 0.00
-10.71 + -3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '10.71' to each side of the equation.
-10.71 + -3x + 10.71 + x2 = 0.00 + 10.71

Reorder the terms:
-10.71 + 10.71 + -3x + x2 = 0.00 + 10.71

Combine like terms: -10.71 + 10.71 = 0.00
0.00 + -3x + x2 = 0.00 + 10.71
-3x + x2 = 0.00 + 10.71

Combine like terms: 0.00 + 10.71 = 10.71
-3x + x2 = 10.71

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 10.71 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 10.71 + 2.25

Combine like terms: 10.71 + 2.25 = 12.96
2.25 + -3x + x2 = 12.96

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 12.96

Calculate the square root of the right side: 3.6

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.6 and -3.6.


Subproblem 1
x + -1.5 = 3.6

Simplifying
x + -1.5 = 3.6

Reorder the terms:
-1.5 + x = 3.6

Solving
-1.5 + x = 3.6

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.6 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.6 + 1.5
x = 3.6 + 1.5

Combine like terms: 3.6 + 1.5 = 5.1
x = 5.1

Simplifying
x = 5.1


Subproblem 2
x + -1.5 = -3.6

Simplifying
x + -1.5 = -3.6

Reorder the terms:
-1.5 + x = -3.6

Solving
-1.5 + x = -3.6

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.6 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.6 + 1.5
x = -3.6 + 1.5

Combine like terms: -3.6 + 1.5 = -2.1
x = -2.1

Simplifying
x = -2.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.1, -2.1}

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