(x+40)(x+10)=600

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Solution for (x+40)(x+10)=600 equation:


Simplifying
(x + 40)(x + 10) = 600

Reorder the terms:
(40 + x)(x + 10) = 600

Reorder the terms:
(40 + x)(10 + x) = 600

Multiply (40 + x) * (10 + x)
(40(10 + x) + x(10 + x)) = 600
((10 * 40 + x * 40) + x(10 + x)) = 600
((400 + 40x) + x(10 + x)) = 600
(400 + 40x + (10 * x + x * x)) = 600
(400 + 40x + (10x + x2)) = 600

Combine like terms: 40x + 10x = 50x
(400 + 50x + x2) = 600

Solving
400 + 50x + x2 = 600

Solving for variable 'x'.

Reorder the terms:
400 + -600 + 50x + x2 = 600 + -600

Combine like terms: 400 + -600 = -200
-200 + 50x + x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-200 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 50x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 50x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 50x + x2 = 0 + 200
50x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
50x + x2 = 200

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 200 + 625

Reorder the terms:
625 + 50x + x2 = 200 + 625

Combine like terms: 200 + 625 = 825
625 + 50x + x2 = 825

Factor a perfect square on the left side:
(x + 25)(x + 25) = 825

Calculate the square root of the right side: 28.722813233

Break this problem into two subproblems by setting 
(x + 25) equal to 28.722813233 and -28.722813233.

Subproblem 1

x + 25 = 28.722813233 Simplifying x + 25 = 28.722813233 Reorder the terms: 25 + x = 28.722813233 Solving 25 + x = 28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 28.722813233 + -25 Combine like terms: 25 + -25 = 0 0 + x = 28.722813233 + -25 x = 28.722813233 + -25 Combine like terms: 28.722813233 + -25 = 3.722813233 x = 3.722813233 Simplifying x = 3.722813233

Subproblem 2

x + 25 = -28.722813233 Simplifying x + 25 = -28.722813233 Reorder the terms: 25 + x = -28.722813233 Solving 25 + x = -28.722813233 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -28.722813233 + -25 Combine like terms: 25 + -25 = 0 0 + x = -28.722813233 + -25 x = -28.722813233 + -25 Combine like terms: -28.722813233 + -25 = -53.722813233 x = -53.722813233 Simplifying x = -53.722813233

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.722813233, -53.722813233}

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