10x(x-15)=-70

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Solution for 10x(x-15)=-70 equation: 


Simplifying
10x(x + -15) = -70

Reorder the terms:
10x(-15 + x) = -70
(-15 * 10x + x * 10x) = -70
(-150x + 10x2) = -70

Solving
-150x + 10x2 = -70

Solving for variable 'x'.

Reorder the terms:
70 + -150x + 10x2 = -70 + 70

Combine like terms: -70 + 70 = 0
70 + -150x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(7 + -15x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(7 + -15x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -15x + x2 = 0

Solving
7 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -15x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -15x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -15x + x2 = 0 + -7
-15x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-15x + x2 = -7

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -7 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -7 + 56.25

Combine like terms: -7 + 56.25 = 49.25
56.25 + -15x + x2 = 49.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.017834424 and -7.017834424.


Subproblem 1
x + -7.5 = 7.017834424

Simplifying
x + -7.5 = 7.017834424

Reorder the terms:
-7.5 + x = 7.017834424

Solving
-7.5 + x = 7.017834424

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 7.017834424 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 7.017834424 + 7.5
x = 7.017834424 + 7.5

Combine like terms: 7.017834424 + 7.5 = 14.517834424
x = 14.517834424

Simplifying
x = 14.517834424


Subproblem 2
x + -7.5 = -7.017834424

Simplifying
x + -7.5 = -7.017834424

Reorder the terms:
-7.5 + x = -7.017834424

Solving
-7.5 + x = -7.017834424

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -7.017834424 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -7.017834424 + 7.5
x = -7.017834424 + 7.5

Combine like terms: -7.017834424 + 7.5 = 0.482165576
x = 0.482165576

Simplifying
x = 0.482165576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.517834424, 0.482165576}
Solution
x = {14.517834424, 0.482165576}

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