2x(x+5)-16=18

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Solution for 2x(x+5)-16=18 equation: 


Simplifying
2x(x + 5) + -16 = 18

Reorder the terms:
2x(5 + x) + -16 = 18
(5 * 2x + x * 2x) + -16 = 18
(10x + 2x2) + -16 = 18

Reorder the terms:
-16 + 10x + 2x2 = 18

Solving
-16 + 10x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
-16 + -18 + 10x + 2x2 = 18 + -18

Combine like terms: -16 + -18 = -34
-34 + 10x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-34 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + 5x + x2 = 0

Solving
-17 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 5x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 5x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 5x + x2 = 0 + 17
5x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
5x + x2 = 17

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 = 17 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 17 + 6.25

Combine like terms: 17 + 6.25 = 23.25
6.25 + 5x + x2 = 23.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + 2.5) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + 2.5 = 4.82182538

Simplifying
x + 2.5 = 4.82182538

Reorder the terms:
2.5 + x = 4.82182538

Solving
2.5 + x = 4.82182538

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 = 4.82182538 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 4.82182538 + -2.5
x = 4.82182538 + -2.5

Combine like terms: 4.82182538 + -2.5 = 2.32182538
x = 2.32182538

Simplifying
x = 2.32182538


Subproblem 2
x + 2.5 = -4.82182538

Simplifying
x + 2.5 = -4.82182538

Reorder the terms:
2.5 + x = -4.82182538

Solving
2.5 + x = -4.82182538

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 = -4.82182538 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -4.82182538 + -2.5
x = -4.82182538 + -2.5

Combine like terms: -4.82182538 + -2.5 = -7.32182538
x = -7.32182538

Simplifying
x = -7.32182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.32182538, -7.32182538}
Solution
x = {2.32182538, -7.32182538}

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