1.3x+2(0.6x-4)=3x-0.5x(x+16)

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Solution for 1.3x+2(0.6x-4)=3x-0.5x(x+16) equation:


Simplifying
1.3x + 2(0.6x + -4) = 3x + -0.5x(x + 16)

Reorder the terms:
1.3x + 2(-4 + 0.6x) = 3x + -0.5x(x + 16)
1.3x + (-4 * 2 + 0.6x * 2) = 3x + -0.5x(x + 16)
1.3x + (-8 + 1.2x) = 3x + -0.5x(x + 16)

Reorder the terms:
-8 + 1.3x + 1.2x = 3x + -0.5x(x + 16)

Combine like terms: 1.3x + 1.2x = 2.5x
-8 + 2.5x = 3x + -0.5x(x + 16)

Reorder the terms:
-8 + 2.5x = 3x + -0.5x(16 + x)
-8 + 2.5x = 3x + (16 * -0.5x + x * -0.5x)
-8 + 2.5x = 3x + (-8x + -0.5x2)

Combine like terms: 3x + -8x = -5x
-8 + 2.5x = -5x + -0.5x2

Solving
-8 + 2.5x = -5x + -0.5x2

Solving for variable 'x'.

Combine like terms: 2.5x + 5x = 7.5x
-8 + 7.5x + 0.5x2 = -5x + -0.5x2 + 5x + 0.5x2

Reorder the terms:
-8 + 7.5x + 0.5x2 = -5x + 5x + -0.5x2 + 0.5x2

Combine like terms: -5x + 5x = 0
-8 + 7.5x + 0.5x2 = 0 + -0.5x2 + 0.5x2
-8 + 7.5x + 0.5x2 = -0.5x2 + 0.5x2

Combine like terms: -0.5x2 + 0.5x2 = 0.0
-8 + 7.5x + 0.5x2 = 0.0

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

Divide each side by '0.5'.
-16 + 15x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 15x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 15x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 15x + x2 = 0 + 16
15x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
15x + x2 = 16

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 16 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 16 + 56.25

Combine like terms: 16 + 56.25 = 72.25
56.25 + 15x + x2 = 72.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 72.25

Calculate the square root of the right side: 8.5

Break this problem into two subproblems by setting 
(x + 7.5) equal to 8.5 and -8.5.

Subproblem 1

x + 7.5 = 8.5 Simplifying x + 7.5 = 8.5 Reorder the terms: 7.5 + x = 8.5 Solving 7.5 + x = 8.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.5 + -7.5 x = 8.5 + -7.5 Combine like terms: 8.5 + -7.5 = 1 x = 1 Simplifying x = 1

Subproblem 2

x + 7.5 = -8.5 Simplifying x + 7.5 = -8.5 Reorder the terms: 7.5 + x = -8.5 Solving 7.5 + x = -8.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.5 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.5 + -7.5 x = -8.5 + -7.5 Combine like terms: -8.5 + -7.5 = -16 x = -16 Simplifying x = -16

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1, -16}

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