5x(x-30)=110

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Solution for 5x(x-30)=110 equation: 


Simplifying
5x(x + -30) = 110

Reorder the terms:
5x(-30 + x) = 110
(-30 * 5x + x * 5x) = 110
(-150x + 5x2) = 110

Solving
-150x + 5x2 = 110

Solving for variable 'x'.

Reorder the terms:
-110 + -150x + 5x2 = 110 + -110

Combine like terms: 110 + -110 = 0
-110 + -150x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-22 + -30x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-22 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
-22 + -30x + x2 = 0

Solving
-22 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -30x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -30x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -30x + x2 = 0 + 22
-30x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-30x + x2 = 22

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 22 + 225

Reorder the terms:
225 + -30x + x2 = 22 + 225

Combine like terms: 22 + 225 = 247
225 + -30x + x2 = 247

Factor a perfect square on the left side:
(x + -15)(x + -15) = 247

Calculate the square root of the right side: 15.716233646

Break this problem into two subproblems by setting 
(x + -15) equal to 15.716233646 and -15.716233646.


Subproblem 1
x + -15 = 15.716233646

Simplifying
x + -15 = 15.716233646

Reorder the terms:
-15 + x = 15.716233646

Solving
-15 + x = 15.716233646

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 15.716233646 + 15

Combine like terms: -15 + 15 = 0
0 + x = 15.716233646 + 15
x = 15.716233646 + 15

Combine like terms: 15.716233646 + 15 = 30.716233646
x = 30.716233646

Simplifying
x = 30.716233646


Subproblem 2
x + -15 = -15.716233646

Simplifying
x + -15 = -15.716233646

Reorder the terms:
-15 + x = -15.716233646

Solving
-15 + x = -15.716233646

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -15.716233646 + 15

Combine like terms: -15 + 15 = 0
0 + x = -15.716233646 + 15
x = -15.716233646 + 15

Combine like terms: -15.716233646 + 15 = -0.716233646
x = -0.716233646

Simplifying
x = -0.716233646


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.716233646, -0.716233646}
Solution
x = {30.716233646, -0.716233646}

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