(x-28)+(2x-16)(.5x+14)=180

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Solution for (x-28)+(2x-16)(.5x+14)=180 equation:


Simplifying
(x + -28) + (2x + -16)(0.5x + 14) = 180

Reorder the terms:
(-28 + x) + (2x + -16)(0.5x + 14) = 180

Remove parenthesis around (-28 + x)
-28 + x + (2x + -16)(0.5x + 14) = 180

Reorder the terms:
-28 + x + (-16 + 2x)(0.5x + 14) = 180

Reorder the terms:
-28 + x + (-16 + 2x)(14 + 0.5x) = 180

Multiply (-16 + 2x) * (14 + 0.5x)
-28 + x + (-16(14 + 0.5x) + 2x * (14 + 0.5x)) = 180
-28 + x + ((14 * -16 + 0.5x * -16) + 2x * (14 + 0.5x)) = 180
-28 + x + ((-224 + -8x) + 2x * (14 + 0.5x)) = 180
-28 + x + (-224 + -8x + (14 * 2x + 0.5x * 2x)) = 180
-28 + x + (-224 + -8x + (28x + 1x2)) = 180

Combine like terms: -8x + 28x = 20x
-28 + x + (-224 + 20x + 1x2) = 180

Reorder the terms:
-28 + -224 + x + 20x + 1x2 = 180

Combine like terms: -28 + -224 = -252
-252 + x + 20x + 1x2 = 180

Combine like terms: x + 20x = 21x
-252 + 21x + 1x2 = 180

Solving
-252 + 21x + 1x2 = 180

Solving for variable 'x'.

Reorder the terms:
-252 + -180 + 21x + 1x2 = 180 + -180

Combine like terms: -252 + -180 = -432
-432 + 21x + 1x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-432 + 21x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '432' to each side of the equation.
-432 + 21x + 432 + x2 = 0 + 432

Reorder the terms:
-432 + 432 + 21x + x2 = 0 + 432

Combine like terms: -432 + 432 = 0
0 + 21x + x2 = 0 + 432
21x + x2 = 0 + 432

Combine like terms: 0 + 432 = 432
21x + x2 = 432

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 432 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 432 + 110.25

Combine like terms: 432 + 110.25 = 542.25
110.25 + 21x + x2 = 542.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 542.25

Calculate the square root of the right side: 23.286262044

Break this problem into two subproblems by setting 
(x + 10.5) equal to 23.286262044 and -23.286262044.

Subproblem 1

x + 10.5 = 23.286262044 Simplifying x + 10.5 = 23.286262044 Reorder the terms: 10.5 + x = 23.286262044 Solving 10.5 + x = 23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 23.286262044 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 23.286262044 + -10.5 x = 23.286262044 + -10.5 Combine like terms: 23.286262044 + -10.5 = 12.786262044 x = 12.786262044 Simplifying x = 12.786262044

Subproblem 2

x + 10.5 = -23.286262044 Simplifying x + 10.5 = -23.286262044 Reorder the terms: 10.5 + x = -23.286262044 Solving 10.5 + x = -23.286262044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -23.286262044 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -23.286262044 + -10.5 x = -23.286262044 + -10.5 Combine like terms: -23.286262044 + -10.5 = -33.786262044 x = -33.786262044 Simplifying x = -33.786262044

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.786262044, -33.786262044}

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