(20-x)(40-x)=526

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Solution for (20-x)(40-x)=526 equation:


Simplifying
(20 + -1x)(40 + -1x) = 526

Multiply (20 + -1x) * (40 + -1x)
(20(40 + -1x) + -1x * (40 + -1x)) = 526
((40 * 20 + -1x * 20) + -1x * (40 + -1x)) = 526
((800 + -20x) + -1x * (40 + -1x)) = 526
(800 + -20x + (40 * -1x + -1x * -1x)) = 526
(800 + -20x + (-40x + 1x2)) = 526

Combine like terms: -20x + -40x = -60x
(800 + -60x + 1x2) = 526

Solving
800 + -60x + 1x2 = 526

Solving for variable 'x'.

Reorder the terms:
800 + -526 + -60x + 1x2 = 526 + -526

Combine like terms: 800 + -526 = 274
274 + -60x + 1x2 = 526 + -526

Combine like terms: 526 + -526 = 0
274 + -60x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-274' to each side of the equation.
274 + -60x + -274 + x2 = 0 + -274

Reorder the terms:
274 + -274 + -60x + x2 = 0 + -274

Combine like terms: 274 + -274 = 0
0 + -60x + x2 = 0 + -274
-60x + x2 = 0 + -274

Combine like terms: 0 + -274 = -274
-60x + x2 = -274

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = -274 + 900

Reorder the terms:
900 + -60x + x2 = -274 + 900

Combine like terms: -274 + 900 = 626
900 + -60x + x2 = 626

Factor a perfect square on the left side:
(x + -30)(x + -30) = 626

Calculate the square root of the right side: 25.019992006

Break this problem into two subproblems by setting 
(x + -30) equal to 25.019992006 and -25.019992006.

Subproblem 1

x + -30 = 25.019992006 Simplifying x + -30 = 25.019992006 Reorder the terms: -30 + x = 25.019992006 Solving -30 + x = 25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 25.019992006 + 30 Combine like terms: -30 + 30 = 0 0 + x = 25.019992006 + 30 x = 25.019992006 + 30 Combine like terms: 25.019992006 + 30 = 55.019992006 x = 55.019992006 Simplifying x = 55.019992006

Subproblem 2

x + -30 = -25.019992006 Simplifying x + -30 = -25.019992006 Reorder the terms: -30 + x = -25.019992006 Solving -30 + x = -25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -25.019992006 + 30 Combine like terms: -30 + 30 = 0 0 + x = -25.019992006 + 30 x = -25.019992006 + 30 Combine like terms: -25.019992006 + 30 = 4.980007994 x = 4.980007994 Simplifying x = 4.980007994

Solution

The solution to the problem is based on the solutions from the subproblems. x = {55.019992006, 4.980007994}

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