150.72=2(3.14)x(5)+2(3.14)x^2

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Solution for 150.72=2(3.14)x(5)+2(3.14)x^2 equation: 


Simplifying
150.72 = 2(3.14) * x(5) + 2(3.14) * x2

Reorder the terms for easier multiplication:
150.72 = 2 * 3.14 * 5x + 2(3.14) * x2

Multiply 2 * 3.14
150.72 = 6.28 * 5x + 2(3.14) * x2

Multiply 6.28 * 5
150.72 = 31.4x + 2(3.14) * x2

Multiply 2 * 3.14
150.72 = 31.4x + 6.28x2

Solving
150.72 = 31.4x + 6.28x2

Solving for variable 'x'.

Reorder the terms:
150.72 + -31.4x + -6.28x2 = 31.4x + -31.4x + 6.28x2 + -6.28x2

Combine like terms: 31.4x + -31.4x = 0.0
150.72 + -31.4x + -6.28x2 = 0.0 + 6.28x2 + -6.28x2
150.72 + -31.4x + -6.28x2 = 6.28x2 + -6.28x2

Combine like terms: 6.28x2 + -6.28x2 = 0.00
150.72 + -31.4x + -6.28x2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-24 + 5x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 5x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 5x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 5x + x2 = 0 + 24
5x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
5x + x2 = 24

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 = 24 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 24 + 6.25

Combine like terms: 24 + 6.25 = 30.25
6.25 + 5x + x2 = 30.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.5 and -5.5.


Subproblem 1
x + 2.5 = 5.5

Simplifying
x + 2.5 = 5.5

Reorder the terms:
2.5 + x = 5.5

Solving
2.5 + x = 5.5

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 = 5.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 5.5 + -2.5
x = 5.5 + -2.5

Combine like terms: 5.5 + -2.5 = 3
x = 3

Simplifying
x = 3


Subproblem 2
x + 2.5 = -5.5

Simplifying
x + 2.5 = -5.5

Reorder the terms:
2.5 + x = -5.5

Solving
2.5 + x = -5.5

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 = -5.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -5.5 + -2.5
x = -5.5 + -2.5

Combine like terms: -5.5 + -2.5 = -8
x = -8

Simplifying
x = -8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3, -8}

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