(x+50)(x+30)=2320

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Solution for (x+50)(x+30)=2320 equation:


Simplifying
(x + 50)(x + 30) = 2320

Reorder the terms:
(50 + x)(x + 30) = 2320

Reorder the terms:
(50 + x)(30 + x) = 2320

Multiply (50 + x) * (30 + x)
(50(30 + x) + x(30 + x)) = 2320
((30 * 50 + x * 50) + x(30 + x)) = 2320
((1500 + 50x) + x(30 + x)) = 2320
(1500 + 50x + (30 * x + x * x)) = 2320
(1500 + 50x + (30x + x2)) = 2320

Combine like terms: 50x + 30x = 80x
(1500 + 80x + x2) = 2320

Solving
1500 + 80x + x2 = 2320

Solving for variable 'x'.

Reorder the terms:
1500 + -2320 + 80x + x2 = 2320 + -2320

Combine like terms: 1500 + -2320 = -820
-820 + 80x + x2 = 2320 + -2320

Combine like terms: 2320 + -2320 = 0
-820 + 80x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '820' to each side of the equation.
-820 + 80x + 820 + x2 = 0 + 820

Reorder the terms:
-820 + 820 + 80x + x2 = 0 + 820

Combine like terms: -820 + 820 = 0
0 + 80x + x2 = 0 + 820
80x + x2 = 0 + 820

Combine like terms: 0 + 820 = 820
80x + x2 = 820

The x term is 80x.  Take half its coefficient (40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
80x + 1600 + x2 = 820 + 1600

Reorder the terms:
1600 + 80x + x2 = 820 + 1600

Combine like terms: 820 + 1600 = 2420
1600 + 80x + x2 = 2420

Factor a perfect square on the left side:
(x + 40)(x + 40) = 2420

Calculate the square root of the right side: 49.193495505

Break this problem into two subproblems by setting 
(x + 40) equal to 49.193495505 and -49.193495505.

Subproblem 1

x + 40 = 49.193495505 Simplifying x + 40 = 49.193495505 Reorder the terms: 40 + x = 49.193495505 Solving 40 + x = 49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 49.193495505 + -40 Combine like terms: 40 + -40 = 0 0 + x = 49.193495505 + -40 x = 49.193495505 + -40 Combine like terms: 49.193495505 + -40 = 9.193495505 x = 9.193495505 Simplifying x = 9.193495505

Subproblem 2

x + 40 = -49.193495505 Simplifying x + 40 = -49.193495505 Reorder the terms: 40 + x = -49.193495505 Solving 40 + x = -49.193495505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -49.193495505 + -40 Combine like terms: 40 + -40 = 0 0 + x = -49.193495505 + -40 x = -49.193495505 + -40 Combine like terms: -49.193495505 + -40 = -89.193495505 x = -89.193495505 Simplifying x = -89.193495505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.193495505, -89.193495505}

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