6=.10x(30+x)

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Solution for 6=.10x(30+x) equation:


Simplifying
6 = 0.10x(30 + x)
6 = (30 * 0.10x + x * 0.10x)
6 = (3x + 0.10x2)

Solving
6 = 3x + 0.10x2

Solving for variable 'x'.

Reorder the terms:
6 + -3x + -0.10x2 = 3x + -3x + 0.10x2 + -0.10x2

Combine like terms: 3x + -3x = 0
6 + -3x + -0.10x2 = 0 + 0.10x2 + -0.10x2
6 + -3x + -0.10x2 = 0.10x2 + -0.10x2

Combine like terms: 0.10x2 + -0.10x2 = 0.00
6 + -3x + -0.10x2 = 0.00

Begin completing the square.  Divide all terms by
-0.10 the coefficient of the squared term: 

Divide each side by '-0.10'.
-60 + 30x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 30x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 30x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 30x + x2 = 0 + 60
30x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
30x + x2 = 60

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 60 + 225

Reorder the terms:
225 + 30x + x2 = 60 + 225

Combine like terms: 60 + 225 = 285
225 + 30x + x2 = 285

Factor a perfect square on the left side:
(x + 15)(x + 15) = 285

Calculate the square root of the right side: 16.881943016

Break this problem into two subproblems by setting 
(x + 15) equal to 16.881943016 and -16.881943016.

Subproblem 1

x + 15 = 16.881943016 Simplifying x + 15 = 16.881943016 Reorder the terms: 15 + x = 16.881943016 Solving 15 + x = 16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.881943016 + -15 x = 16.881943016 + -15 Combine like terms: 16.881943016 + -15 = 1.881943016 x = 1.881943016 Simplifying x = 1.881943016

Subproblem 2

x + 15 = -16.881943016 Simplifying x + 15 = -16.881943016 Reorder the terms: 15 + x = -16.881943016 Solving 15 + x = -16.881943016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.881943016 + -15 x = -16.881943016 + -15 Combine like terms: -16.881943016 + -15 = -31.881943016 x = -31.881943016 Simplifying x = -31.881943016

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.881943016, -31.881943016}

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