-10x(x+5)+66=-17-17

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Solution for -10x(x+5)+66=-17-17 equation: 


Simplifying
-10x(x + 5) + 66 = -17 + -17

Reorder the terms:
-10x(5 + x) + 66 = -17 + -17
(5 * -10x + x * -10x) + 66 = -17 + -17
(-50x + -10x2) + 66 = -17 + -17

Reorder the terms:
66 + -50x + -10x2 = -17 + -17

Combine like terms: -17 + -17 = -34
66 + -50x + -10x2 = -34

Solving
66 + -50x + -10x2 = -34

Solving for variable 'x'.

Reorder the terms:
66 + 34 + -50x + -10x2 = -34 + 34

Combine like terms: 66 + 34 = 100
100 + -50x + -10x2 = -34 + 34

Combine like terms: -34 + 34 = 0
100 + -50x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(10 + -5x + -1x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(10 + -5x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -5x + -1x2 = 0

Solving
10 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 5x + x2 = 0 + 10
5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
5x + x2 = 10

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 10 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 10 + 6.25

Combine like terms: 10 + 6.25 = 16.25
6.25 + 5x + x2 = 16.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x + 2.5 = 4.031128874

Simplifying
x + 2.5 = 4.031128874

Reorder the terms:
2.5 + x = 4.031128874

Solving
2.5 + x = 4.031128874

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 4.031128874 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.031128874 + -2.5
x = 4.031128874 + -2.5

Combine like terms: 4.031128874 + -2.5 = 1.531128874
x = 1.531128874

Simplifying
x = 1.531128874


Subproblem 2
x + 2.5 = -4.031128874

Simplifying
x + 2.5 = -4.031128874

Reorder the terms:
2.5 + x = -4.031128874

Solving
2.5 + x = -4.031128874

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -4.031128874 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.031128874 + -2.5
x = -4.031128874 + -2.5

Combine like terms: -4.031128874 + -2.5 = -6.531128874
x = -6.531128874

Simplifying
x = -6.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.531128874, -6.531128874}
Solution
x = {1.531128874, -6.531128874}

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