200=5x^2+10x+15

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Solution for 200=5x^2+10x+15 equation: 


Simplifying
200 = 5x2 + 10x + 15

Reorder the terms:
200 = 15 + 10x + 5x2

Solving
200 = 15 + 10x + 5x2

Solving for variable 'x'.

Combine like terms: 200 + -15 = 185
185 + -10x + -5x2 = 15 + 10x + 5x2 + -15 + -10x + -5x2

Reorder the terms:
185 + -10x + -5x2 = 15 + -15 + 10x + -10x + 5x2 + -5x2

Combine like terms: 15 + -15 = 0
185 + -10x + -5x2 = 0 + 10x + -10x + 5x2 + -5x2
185 + -10x + -5x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
185 + -10x + -5x2 = 0 + 5x2 + -5x2
185 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
185 + -10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(37 + -2x + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(37 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
37 + -2x + -1x2 = 0

Solving
37 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-37 + 2x + x2 = 0

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 2x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 2x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 2x + x2 = 0 + 37
2x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
2x + x2 = 37

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 37 + 1

Reorder the terms:
1 + 2x + x2 = 37 + 1

Combine like terms: 37 + 1 = 38
1 + 2x + x2 = 38

Factor a perfect square on the left side:
(x + 1)(x + 1) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + 1) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + 1 = 6.164414003

Simplifying
x + 1 = 6.164414003

Reorder the terms:
1 + x = 6.164414003

Solving
1 + x = 6.164414003

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.164414003 + -1
x = 6.164414003 + -1

Combine like terms: 6.164414003 + -1 = 5.164414003
x = 5.164414003

Simplifying
x = 5.164414003


Subproblem 2
x + 1 = -6.164414003

Simplifying
x + 1 = -6.164414003

Reorder the terms:
1 + x = -6.164414003

Solving
1 + x = -6.164414003

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.164414003 + -1
x = -6.164414003 + -1

Combine like terms: -6.164414003 + -1 = -7.164414003
x = -7.164414003

Simplifying
x = -7.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.164414003, -7.164414003}
Solution
x = {5.164414003, -7.164414003}

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