(3x+17)(55-x)=90

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Solution for (3x+17)(55-x)=90 equation:


Simplifying
(3x + 17)(55 + -1x) = 90

Reorder the terms:
(17 + 3x)(55 + -1x) = 90

Multiply (17 + 3x) * (55 + -1x)
(17(55 + -1x) + 3x * (55 + -1x)) = 90
((55 * 17 + -1x * 17) + 3x * (55 + -1x)) = 90
((935 + -17x) + 3x * (55 + -1x)) = 90
(935 + -17x + (55 * 3x + -1x * 3x)) = 90
(935 + -17x + (165x + -3x2)) = 90

Combine like terms: -17x + 165x = 148x
(935 + 148x + -3x2) = 90

Solving
935 + 148x + -3x2 = 90

Solving for variable 'x'.

Reorder the terms:
935 + -90 + 148x + -3x2 = 90 + -90

Combine like terms: 935 + -90 = 845
845 + 148x + -3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
845 + 148x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-281.6666667 + -49.33333333x + x2 = 0

Move the constant term to the right:

Add '281.6666667' to each side of the equation.
-281.6666667 + -49.33333333x + 281.6666667 + x2 = 0 + 281.6666667

Reorder the terms:
-281.6666667 + 281.6666667 + -49.33333333x + x2 = 0 + 281.6666667

Combine like terms: -281.6666667 + 281.6666667 = 0.0000000
0.0000000 + -49.33333333x + x2 = 0 + 281.6666667
-49.33333333x + x2 = 0 + 281.6666667

Combine like terms: 0 + 281.6666667 = 281.6666667
-49.33333333x + x2 = 281.6666667

The x term is -49.33333333x.  Take half its coefficient (-24.66666667).
Square it (608.4444446) and add it to both sides.

Add '608.4444446' to each side of the equation.
-49.33333333x + 608.4444446 + x2 = 281.6666667 + 608.4444446

Reorder the terms:
608.4444446 + -49.33333333x + x2 = 281.6666667 + 608.4444446

Combine like terms: 281.6666667 + 608.4444446 = 890.1111113
608.4444446 + -49.33333333x + x2 = 890.1111113

Factor a perfect square on the left side:
(x + -24.66666667)(x + -24.66666667) = 890.1111113

Calculate the square root of the right side: 29.834729952

Break this problem into two subproblems by setting 
(x + -24.66666667) equal to 29.834729952 and -29.834729952.

Subproblem 1

x + -24.66666667 = 29.834729952 Simplifying x + -24.66666667 = 29.834729952 Reorder the terms: -24.66666667 + x = 29.834729952 Solving -24.66666667 + x = 29.834729952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.66666667' to each side of the equation. -24.66666667 + 24.66666667 + x = 29.834729952 + 24.66666667 Combine like terms: -24.66666667 + 24.66666667 = 0.00000000 0.00000000 + x = 29.834729952 + 24.66666667 x = 29.834729952 + 24.66666667 Combine like terms: 29.834729952 + 24.66666667 = 54.501396622 x = 54.501396622 Simplifying x = 54.501396622

Subproblem 2

x + -24.66666667 = -29.834729952 Simplifying x + -24.66666667 = -29.834729952 Reorder the terms: -24.66666667 + x = -29.834729952 Solving -24.66666667 + x = -29.834729952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.66666667' to each side of the equation. -24.66666667 + 24.66666667 + x = -29.834729952 + 24.66666667 Combine like terms: -24.66666667 + 24.66666667 = 0.00000000 0.00000000 + x = -29.834729952 + 24.66666667 x = -29.834729952 + 24.66666667 Combine like terms: -29.834729952 + 24.66666667 = -5.168063282 x = -5.168063282 Simplifying x = -5.168063282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {54.501396622, -5.168063282}

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