x+(x*.15x)=375

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Solution for x+(x*.15x)=375 equation:


Simplifying
x + (x * 0.15x) = 375

Reorder the terms for easier multiplication:
x + (0.15x * x) = 375

Multiply x * x
x + (0.15x2) = 375

Solving
x + (0.15x2) = 375

Solving for variable 'x'.

Reorder the terms:
-375 + x + (0.15x2) = 375 + -375

Combine like terms: 375 + -375 = 0
-375 + x + (0.15x2) = 0

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

Divide each side by '0.15'.
-2500 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '2500' to each side of the equation.
-2500 + 6.666666667x + 2500 + x2 = 0 + 2500

Reorder the terms:
-2500 + 2500 + 6.666666667x + x2 = 0 + 2500

Combine like terms: -2500 + 2500 = 0
0 + 6.666666667x + x2 = 0 + 2500
6.666666667x + x2 = 0 + 2500

Combine like terms: 0 + 2500 = 2500
6.666666667x + x2 = 2500

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.
6.666666667x + 0.25 + x2 = 2500 + 0.25

Reorder the terms:
0.25 + 6.666666667x + x2 = 2500 + 0.25

Combine like terms: 2500 + 0.25 = 2500.25
0.25 + 6.666666667x + x2 = 2500.25

Factor a perfect square on the left side:
((x) + 0.5)((x) + 0.5) = 2500.25

Calculate the square root of the right side: 50.002499938

Break this problem into two subproblems by setting 
((x) + 0.5) equal to 50.002499938 and -50.002499938.

Subproblem 1

(x) + 0.5 = 50.002499938 Simplifying (x) + 0.5 = 50.002499938 x + 0.5 = 50.002499938 Reorder the terms: 0.5 + x = 50.002499938 Solving 0.5 + x = 50.002499938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 50.002499938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 50.002499938 + -0.5 x = 50.002499938 + -0.5 Combine like terms: 50.002499938 + -0.5 = 49.502499938 x = 49.502499938 Simplifying x = 49.502499938

Subproblem 2

(x) + 0.5 = -50.002499938 Simplifying (x) + 0.5 = -50.002499938 x + 0.5 = -50.002499938 Reorder the terms: 0.5 + x = -50.002499938 Solving 0.5 + x = -50.002499938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -50.002499938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -50.002499938 + -0.5 x = -50.002499938 + -0.5 Combine like terms: -50.002499938 + -0.5 = -50.502499938 x = -50.502499938 Simplifying x = -50.502499938

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.502499938, -50.502499938}

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