x(.0825+x)=300

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Solution for x(.0825+x)=300 equation:


Simplifying
x(0.0825 + x) = 300
(0.0825 * x + x * x) = 300
(0.0825x + x2) = 300

Solving
0.0825x + x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 0.0825x + x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 0.0825x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + 0.0825x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + 0.0825x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + 0.0825x + x2 = 0 + 300
0.0825x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
0.0825x + x2 = 300

The x term is 0.0825x.  Take half its coefficient (0.04125).
Square it (0.0017015625) and add it to both sides.

Add '0.0017015625' to each side of the equation.
0.0825x + 0.0017015625 + x2 = 300 + 0.0017015625

Reorder the terms:
0.0017015625 + 0.0825x + x2 = 300 + 0.0017015625

Combine like terms: 300 + 0.0017015625 = 300.0017015625
0.0017015625 + 0.0825x + x2 = 300.0017015625

Factor a perfect square on the left side:
(x + 0.04125)(x + 0.04125) = 300.0017015625

Calculate the square root of the right side: 17.320557195

Break this problem into two subproblems by setting 
(x + 0.04125) equal to 17.320557195 and -17.320557195.

Subproblem 1

x + 0.04125 = 17.320557195 Simplifying x + 0.04125 = 17.320557195 Reorder the terms: 0.04125 + x = 17.320557195 Solving 0.04125 + x = 17.320557195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + x = 17.320557195 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + x = 17.320557195 + -0.04125 x = 17.320557195 + -0.04125 Combine like terms: 17.320557195 + -0.04125 = 17.279307195 x = 17.279307195 Simplifying x = 17.279307195

Subproblem 2

x + 0.04125 = -17.320557195 Simplifying x + 0.04125 = -17.320557195 Reorder the terms: 0.04125 + x = -17.320557195 Solving 0.04125 + x = -17.320557195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + x = -17.320557195 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + x = -17.320557195 + -0.04125 x = -17.320557195 + -0.04125 Combine like terms: -17.320557195 + -0.04125 = -17.361807195 x = -17.361807195 Simplifying x = -17.361807195

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.279307195, -17.361807195}

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