x(x+5)=(2x+10)(x-2)+190

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Solution for x(x+5)=(2x+10)(x-2)+190 equation: 


Simplifying
x(x + 5) = (2x + 10)(x + -2) + 190

Reorder the terms:
x(5 + x) = (2x + 10)(x + -2) + 190
(5 * x + x * x) = (2x + 10)(x + -2) + 190
(5x + x2) = (2x + 10)(x + -2) + 190

Reorder the terms:
5x + x2 = (10 + 2x)(x + -2) + 190

Reorder the terms:
5x + x2 = (10 + 2x)(-2 + x) + 190

Multiply (10 + 2x) * (-2 + x)
5x + x2 = (10(-2 + x) + 2x * (-2 + x)) + 190
5x + x2 = ((-2 * 10 + x * 10) + 2x * (-2 + x)) + 190
5x + x2 = ((-20 + 10x) + 2x * (-2 + x)) + 190
5x + x2 = (-20 + 10x + (-2 * 2x + x * 2x)) + 190
5x + x2 = (-20 + 10x + (-4x + 2x2)) + 190

Combine like terms: 10x + -4x = 6x
5x + x2 = (-20 + 6x + 2x2) + 190

Reorder the terms:
5x + x2 = -20 + 190 + 6x + 2x2

Combine like terms: -20 + 190 = 170
5x + x2 = 170 + 6x + 2x2

Solving
5x + x2 = 170 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-170 + 5x + -6x + x2 + -2x2 = 170 + 6x + 2x2 + -170 + -6x + -2x2

Combine like terms: 5x + -6x = -1x
-170 + -1x + x2 + -2x2 = 170 + 6x + 2x2 + -170 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-170 + -1x + -1x2 = 170 + 6x + 2x2 + -170 + -6x + -2x2

Reorder the terms:
-170 + -1x + -1x2 = 170 + -170 + 6x + -6x + 2x2 + -2x2

Combine like terms: 170 + -170 = 0
-170 + -1x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
-170 + -1x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-170 + -1x + -1x2 = 0 + 2x2 + -2x2
-170 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-170 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(170 + x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(170 + x + x2)' equal to zero and attempt to solve:

Simplifying
170 + x + x2 = 0

Solving
170 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-170' to each side of the equation.
170 + x + -170 + x2 = 0 + -170

Reorder the terms:
170 + -170 + x + x2 = 0 + -170

Combine like terms: 170 + -170 = 0
0 + x + x2 = 0 + -170
x + x2 = 0 + -170

Combine like terms: 0 + -170 = -170
x + x2 = -170

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -170 + 0.25

Reorder the terms:
0.25 + x + x2 = -170 + 0.25

Combine like terms: -170 + 0.25 = -169.75
0.25 + x + x2 = -169.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -169.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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