5x(x-16)=45

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Solution for 5x(x-16)=45 equation: 


Simplifying
5x(x + -16) = 45

Reorder the terms:
5x(-16 + x) = 45
(-16 * 5x + x * 5x) = 45
(-80x + 5x2) = 45

Solving
-80x + 5x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -80x + 5x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -80x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + -16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-9 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-9 + -16x + x2 = 0

Solving
-9 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -16x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -16x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -16x + x2 = 0 + 9
-16x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-16x + x2 = 9

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 9 + 64

Reorder the terms:
64 + -16x + x2 = 9 + 64

Combine like terms: 9 + 64 = 73
64 + -16x + x2 = 73

Factor a perfect square on the left side:
(x + -8)(x + -8) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + -8) equal to 8.544003745 and -8.544003745.


Subproblem 1
x + -8 = 8.544003745

Simplifying
x + -8 = 8.544003745

Reorder the terms:
-8 + x = 8.544003745

Solving
-8 + x = 8.544003745

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 8.544003745 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.544003745 + 8
x = 8.544003745 + 8

Combine like terms: 8.544003745 + 8 = 16.544003745
x = 16.544003745

Simplifying
x = 16.544003745


Subproblem 2
x + -8 = -8.544003745

Simplifying
x + -8 = -8.544003745

Reorder the terms:
-8 + x = -8.544003745

Solving
-8 + x = -8.544003745

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -8.544003745 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.544003745 + 8
x = -8.544003745 + 8

Combine like terms: -8.544003745 + 8 = -0.544003745
x = -0.544003745

Simplifying
x = -0.544003745


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.544003745, -0.544003745}
Solution
x = {16.544003745, -0.544003745}

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