2x-10=x(x+5)

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


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

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

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

Solving
-10 + 2x = 5x + x2

Solving for variable 'x'.

Combine like terms: 2x + -5x = -3x
-10 + -3x + -1x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
-10 + -3x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-10 + -3x + -1x2 = 0 + x2 + -1x2
-10 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 3x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 3x + x2 = 0

Solving
10 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x + x2 = 0 + -10
3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
3x + x2 = -10

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -10 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + 3x + x2 = -7.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -7.75

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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