-.10(44)+.35x=.05x(x-16)

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Solution for -.10(44)+.35x=.05x(x-16) equation:


Simplifying
-0.10(44) + 0.35x = 0.05x(x + -16)

Multiply -0.10 * 44
-4.4 + 0.35x = 0.05x(x + -16)

Reorder the terms:
-4.4 + 0.35x = 0.05x(-16 + x)
-4.4 + 0.35x = (-16 * 0.05x + x * 0.05x)
-4.4 + 0.35x = (-0.8x + 0.05x2)

Solving
-4.4 + 0.35x = -0.8x + 0.05x2

Solving for variable 'x'.

Combine like terms: 0.35x + 0.8x = 1.15x
-4.4 + 1.15x + -0.05x2 = -0.8x + 0.05x2 + 0.8x + -0.05x2

Reorder the terms:
-4.4 + 1.15x + -0.05x2 = -0.8x + 0.8x + 0.05x2 + -0.05x2

Combine like terms: -0.8x + 0.8x = 0.0
-4.4 + 1.15x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2
-4.4 + 1.15x + -0.05x2 = 0.05x2 + -0.05x2

Combine like terms: 0.05x2 + -0.05x2 = 0.00
-4.4 + 1.15x + -0.05x2 = 0.00

Begin completing the square.  Divide all terms by
-0.05 the coefficient of the squared term: 

Divide each side by '-0.05'.
88 + -23x + x2 = 0

Move the constant term to the right:

Add '-88' to each side of the equation.
88 + -23x + -88 + x2 = 0 + -88

Reorder the terms:
88 + -88 + -23x + x2 = 0 + -88

Combine like terms: 88 + -88 = 0
0 + -23x + x2 = 0 + -88
-23x + x2 = 0 + -88

Combine like terms: 0 + -88 = -88
-23x + x2 = -88

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -88 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -88 + 132.25

Combine like terms: -88 + 132.25 = 44.25
132.25 + -23x + x2 = 44.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + -11.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x + -11.5 = 6.652067348 Simplifying x + -11.5 = 6.652067348 Reorder the terms: -11.5 + x = 6.652067348 Solving -11.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 6.652067348 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 6.652067348 + 11.5 x = 6.652067348 + 11.5 Combine like terms: 6.652067348 + 11.5 = 18.152067348 x = 18.152067348 Simplifying x = 18.152067348

Subproblem 2

x + -11.5 = -6.652067348 Simplifying x + -11.5 = -6.652067348 Reorder the terms: -11.5 + x = -6.652067348 Solving -11.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -6.652067348 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -6.652067348 + 11.5 x = -6.652067348 + 11.5 Combine like terms: -6.652067348 + 11.5 = 4.847932652 x = 4.847932652 Simplifying x = 4.847932652

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.152067348, 4.847932652}

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