3x(x-10)=45

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Solution for 3x(x-10)=45 equation: 


Simplifying
3x(x + -10) = 45

Reorder the terms:
3x(-10 + x) = 45
(-10 * 3x + x * 3x) = 45
(-30x + 3x2) = 45

Solving
-30x + 3x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -30x + 3x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-15 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -10x + x2 = 0

Solving
-15 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -10x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -10x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -10x + x2 = 0 + 15
-10x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-10x + x2 = 15

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 15 + 25

Reorder the terms:
25 + -10x + x2 = 15 + 25

Combine like terms: 15 + 25 = 40
25 + -10x + x2 = 40

Factor a perfect square on the left side:
(x + -5)(x + -5) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -5) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -5 = 6.32455532

Simplifying
x + -5 = 6.32455532

Reorder the terms:
-5 + x = 6.32455532

Solving
-5 + x = 6.32455532

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 6.32455532 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.32455532 + 5
x = 6.32455532 + 5

Combine like terms: 6.32455532 + 5 = 11.32455532
x = 11.32455532

Simplifying
x = 11.32455532


Subproblem 2
x + -5 = -6.32455532

Simplifying
x + -5 = -6.32455532

Reorder the terms:
-5 + x = -6.32455532

Solving
-5 + x = -6.32455532

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -6.32455532 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.32455532 + 5
x = -6.32455532 + 5

Combine like terms: -6.32455532 + 5 = -1.32455532
x = -1.32455532

Simplifying
x = -1.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.32455532, -1.32455532}
Solution
x = {11.32455532, -1.32455532}

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