x+(5+x)(2x+10)=180

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Solution for x+(5+x)(2x+10)=180 equation:


Simplifying
x + (5 + x)(2x + 10) = 180

Reorder the terms:
x + (5 + x)(10 + 2x) = 180

Multiply (5 + x) * (10 + 2x)
x + (5(10 + 2x) + x(10 + 2x)) = 180
x + ((10 * 5 + 2x * 5) + x(10 + 2x)) = 180
x + ((50 + 10x) + x(10 + 2x)) = 180
x + (50 + 10x + (10 * x + 2x * x)) = 180
x + (50 + 10x + (10x + 2x2)) = 180

Combine like terms: 10x + 10x = 20x
x + (50 + 20x + 2x2) = 180

Reorder the terms:
50 + x + 20x + 2x2 = 180

Combine like terms: x + 20x = 21x
50 + 21x + 2x2 = 180

Solving
50 + 21x + 2x2 = 180

Solving for variable 'x'.

Reorder the terms:
50 + -180 + 21x + 2x2 = 180 + -180

Combine like terms: 50 + -180 = -130
-130 + 21x + 2x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-130 + 21x + 2x2 = 0

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

Divide each side by '2'.
-65 + 10.5x + x2 = 0

Move the constant term to the right:

Add '65' to each side of the equation.
-65 + 10.5x + 65 + x2 = 0 + 65

Reorder the terms:
-65 + 65 + 10.5x + x2 = 0 + 65

Combine like terms: -65 + 65 = 0
0 + 10.5x + x2 = 0 + 65
10.5x + x2 = 0 + 65

Combine like terms: 0 + 65 = 65
10.5x + x2 = 65

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 65 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 65 + 27.5625

Combine like terms: 65 + 27.5625 = 92.5625
27.5625 + 10.5x + x2 = 92.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 92.5625

Calculate the square root of the right side: 9.620940702

Break this problem into two subproblems by setting 
(x + 5.25) equal to 9.620940702 and -9.620940702.

Subproblem 1

x + 5.25 = 9.620940702 Simplifying x + 5.25 = 9.620940702 Reorder the terms: 5.25 + x = 9.620940702 Solving 5.25 + x = 9.620940702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 9.620940702 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 9.620940702 + -5.25 x = 9.620940702 + -5.25 Combine like terms: 9.620940702 + -5.25 = 4.370940702 x = 4.370940702 Simplifying x = 4.370940702

Subproblem 2

x + 5.25 = -9.620940702 Simplifying x + 5.25 = -9.620940702 Reorder the terms: 5.25 + x = -9.620940702 Solving 5.25 + x = -9.620940702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -9.620940702 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -9.620940702 + -5.25 x = -9.620940702 + -5.25 Combine like terms: -9.620940702 + -5.25 = -14.870940702 x = -14.870940702 Simplifying x = -14.870940702

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.370940702, -14.870940702}

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