(2x+20)(x+30)=825

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Solution for (2x+20)(x+30)=825 equation:


Simplifying
(2x + 20)(x + 30) = 825

Reorder the terms:
(20 + 2x)(x + 30) = 825

Reorder the terms:
(20 + 2x)(30 + x) = 825

Multiply (20 + 2x) * (30 + x)
(20(30 + x) + 2x * (30 + x)) = 825
((30 * 20 + x * 20) + 2x * (30 + x)) = 825
((600 + 20x) + 2x * (30 + x)) = 825
(600 + 20x + (30 * 2x + x * 2x)) = 825
(600 + 20x + (60x + 2x2)) = 825

Combine like terms: 20x + 60x = 80x
(600 + 80x + 2x2) = 825

Solving
600 + 80x + 2x2 = 825

Solving for variable 'x'.

Reorder the terms:
600 + -825 + 80x + 2x2 = 825 + -825

Combine like terms: 600 + -825 = -225
-225 + 80x + 2x2 = 825 + -825

Combine like terms: 825 + -825 = 0
-225 + 80x + 2x2 = 0

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

Divide each side by '2'.
-112.5 + 40x + x2 = 0

Move the constant term to the right:

Add '112.5' to each side of the equation.
-112.5 + 40x + 112.5 + x2 = 0 + 112.5

Reorder the terms:
-112.5 + 112.5 + 40x + x2 = 0 + 112.5

Combine like terms: -112.5 + 112.5 = 0.0
0.0 + 40x + x2 = 0 + 112.5
40x + x2 = 0 + 112.5

Combine like terms: 0 + 112.5 = 112.5
40x + x2 = 112.5

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 112.5 + 400

Reorder the terms:
400 + 40x + x2 = 112.5 + 400

Combine like terms: 112.5 + 400 = 512.5
400 + 40x + x2 = 512.5

Factor a perfect square on the left side:
(x + 20)(x + 20) = 512.5

Calculate the square root of the right side: 22.638462845

Break this problem into two subproblems by setting 
(x + 20) equal to 22.638462845 and -22.638462845.

Subproblem 1

x + 20 = 22.638462845 Simplifying x + 20 = 22.638462845 Reorder the terms: 20 + x = 22.638462845 Solving 20 + x = 22.638462845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 22.638462845 + -20 Combine like terms: 20 + -20 = 0 0 + x = 22.638462845 + -20 x = 22.638462845 + -20 Combine like terms: 22.638462845 + -20 = 2.638462845 x = 2.638462845 Simplifying x = 2.638462845

Subproblem 2

x + 20 = -22.638462845 Simplifying x + 20 = -22.638462845 Reorder the terms: 20 + x = -22.638462845 Solving 20 + x = -22.638462845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -22.638462845 + -20 Combine like terms: 20 + -20 = 0 0 + x = -22.638462845 + -20 x = -22.638462845 + -20 Combine like terms: -22.638462845 + -20 = -42.638462845 x = -42.638462845 Simplifying x = -42.638462845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.638462845, -42.638462845}

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