844=(25-x)(40-x)

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Solution for 844=(25-x)(40-x) equation:


Simplifying
844 = (25 + -1x)(40 + -1x)

Multiply (25 + -1x) * (40 + -1x)
844 = (25(40 + -1x) + -1x * (40 + -1x))
844 = ((40 * 25 + -1x * 25) + -1x * (40 + -1x))
844 = ((1000 + -25x) + -1x * (40 + -1x))
844 = (1000 + -25x + (40 * -1x + -1x * -1x))
844 = (1000 + -25x + (-40x + 1x2))

Combine like terms: -25x + -40x = -65x
844 = (1000 + -65x + 1x2)

Solving
844 = 1000 + -65x + 1x2

Solving for variable 'x'.

Combine like terms: 844 + -1000 = -156
-156 + 65x + -1x2 = 1000 + -65x + 1x2 + -1000 + 65x + -1x2

Reorder the terms:
-156 + 65x + -1x2 = 1000 + -1000 + -65x + 65x + 1x2 + -1x2

Combine like terms: 1000 + -1000 = 0
-156 + 65x + -1x2 = 0 + -65x + 65x + 1x2 + -1x2
-156 + 65x + -1x2 = -65x + 65x + 1x2 + -1x2

Combine like terms: -65x + 65x = 0
-156 + 65x + -1x2 = 0 + 1x2 + -1x2
-156 + 65x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-156 + 65x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
156 + -65x + x2 = 0

Move the constant term to the right:

Add '-156' to each side of the equation.
156 + -65x + -156 + x2 = 0 + -156

Reorder the terms:
156 + -156 + -65x + x2 = 0 + -156

Combine like terms: 156 + -156 = 0
0 + -65x + x2 = 0 + -156
-65x + x2 = 0 + -156

Combine like terms: 0 + -156 = -156
-65x + x2 = -156

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = -156 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = -156 + 1056.25

Combine like terms: -156 + 1056.25 = 900.25
1056.25 + -65x + x2 = 900.25

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 900.25

Calculate the square root of the right side: 30.004166377

Break this problem into two subproblems by setting 
(x + -32.5) equal to 30.004166377 and -30.004166377.

Subproblem 1

x + -32.5 = 30.004166377 Simplifying x + -32.5 = 30.004166377 Reorder the terms: -32.5 + x = 30.004166377 Solving -32.5 + x = 30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = 30.004166377 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 30.004166377 + 32.5 x = 30.004166377 + 32.5 Combine like terms: 30.004166377 + 32.5 = 62.504166377 x = 62.504166377 Simplifying x = 62.504166377

Subproblem 2

x + -32.5 = -30.004166377 Simplifying x + -32.5 = -30.004166377 Reorder the terms: -32.5 + x = -30.004166377 Solving -32.5 + x = -30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = -30.004166377 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -30.004166377 + 32.5 x = -30.004166377 + 32.5 Combine like terms: -30.004166377 + 32.5 = 2.495833623 x = 2.495833623 Simplifying x = 2.495833623

Solution

The solution to the problem is based on the solutions from the subproblems. x = {62.504166377, 2.495833623}

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