7x(x+20)=180

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Solution for 7x(x+20)=180 equation:


Simplifying
7x(x + 20) = 180

Reorder the terms:
7x(20 + x) = 180
(20 * 7x + x * 7x) = 180
(140x + 7x2) = 180

Solving
140x + 7x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 140x + 7x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 140x + 7x2 = 0

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

Divide each side by '7'.
-25.71428571 + 20x + x2 = 0

Move the constant term to the right:

Add '25.71428571' to each side of the equation.
-25.71428571 + 20x + 25.71428571 + x2 = 0 + 25.71428571

Reorder the terms:
-25.71428571 + 25.71428571 + 20x + x2 = 0 + 25.71428571

Combine like terms: -25.71428571 + 25.71428571 = 0.00000000
0.00000000 + 20x + x2 = 0 + 25.71428571
20x + x2 = 0 + 25.71428571

Combine like terms: 0 + 25.71428571 = 25.71428571
20x + x2 = 25.71428571

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 25.71428571 + 100

Reorder the terms:
100 + 20x + x2 = 25.71428571 + 100

Combine like terms: 25.71428571 + 100 = 125.71428571
100 + 20x + x2 = 125.71428571

Factor a perfect square on the left side:
(x + 10)(x + 10) = 125.71428571

Calculate the square root of the right side: 11.212238211

Break this problem into two subproblems by setting 
(x + 10) equal to 11.212238211 and -11.212238211.

Subproblem 1

x + 10 = 11.212238211 Simplifying x + 10 = 11.212238211 Reorder the terms: 10 + x = 11.212238211 Solving 10 + x = 11.212238211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.212238211 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.212238211 + -10 x = 11.212238211 + -10 Combine like terms: 11.212238211 + -10 = 1.212238211 x = 1.212238211 Simplifying x = 1.212238211

Subproblem 2

x + 10 = -11.212238211 Simplifying x + 10 = -11.212238211 Reorder the terms: 10 + x = -11.212238211 Solving 10 + x = -11.212238211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.212238211 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.212238211 + -10 x = -11.212238211 + -10 Combine like terms: -11.212238211 + -10 = -21.212238211 x = -21.212238211 Simplifying x = -21.212238211

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.212238211, -21.212238211}

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