(25+2x)(15+x)=750

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Solution for (25+2x)(15+x)=750 equation:


Simplifying
(25 + 2x)(15 + x) = 750

Multiply (25 + 2x) * (15 + x)
(25(15 + x) + 2x * (15 + x)) = 750
((15 * 25 + x * 25) + 2x * (15 + x)) = 750
((375 + 25x) + 2x * (15 + x)) = 750
(375 + 25x + (15 * 2x + x * 2x)) = 750
(375 + 25x + (30x + 2x2)) = 750

Combine like terms: 25x + 30x = 55x
(375 + 55x + 2x2) = 750

Solving
375 + 55x + 2x2 = 750

Solving for variable 'x'.

Reorder the terms:
375 + -750 + 55x + 2x2 = 750 + -750

Combine like terms: 375 + -750 = -375
-375 + 55x + 2x2 = 750 + -750

Combine like terms: 750 + -750 = 0
-375 + 55x + 2x2 = 0

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

Divide each side by '2'.
-187.5 + 27.5x + x2 = 0

Move the constant term to the right:

Add '187.5' to each side of the equation.
-187.5 + 27.5x + 187.5 + x2 = 0 + 187.5

Reorder the terms:
-187.5 + 187.5 + 27.5x + x2 = 0 + 187.5

Combine like terms: -187.5 + 187.5 = 0.0
0.0 + 27.5x + x2 = 0 + 187.5
27.5x + x2 = 0 + 187.5

Combine like terms: 0 + 187.5 = 187.5
27.5x + x2 = 187.5

The x term is 27.5x.  Take half its coefficient (13.75).
Square it (189.0625) and add it to both sides.

Add '189.0625' to each side of the equation.
27.5x + 189.0625 + x2 = 187.5 + 189.0625

Reorder the terms:
189.0625 + 27.5x + x2 = 187.5 + 189.0625

Combine like terms: 187.5 + 189.0625 = 376.5625
189.0625 + 27.5x + x2 = 376.5625

Factor a perfect square on the left side:
(x + 13.75)(x + 13.75) = 376.5625

Calculate the square root of the right side: 19.40521837

Break this problem into two subproblems by setting 
(x + 13.75) equal to 19.40521837 and -19.40521837.

Subproblem 1

x + 13.75 = 19.40521837 Simplifying x + 13.75 = 19.40521837 Reorder the terms: 13.75 + x = 19.40521837 Solving 13.75 + x = 19.40521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = 19.40521837 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = 19.40521837 + -13.75 x = 19.40521837 + -13.75 Combine like terms: 19.40521837 + -13.75 = 5.65521837 x = 5.65521837 Simplifying x = 5.65521837

Subproblem 2

x + 13.75 = -19.40521837 Simplifying x + 13.75 = -19.40521837 Reorder the terms: 13.75 + x = -19.40521837 Solving 13.75 + x = -19.40521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.75' to each side of the equation. 13.75 + -13.75 + x = -19.40521837 + -13.75 Combine like terms: 13.75 + -13.75 = 0.00 0.00 + x = -19.40521837 + -13.75 x = -19.40521837 + -13.75 Combine like terms: -19.40521837 + -13.75 = -33.15521837 x = -33.15521837 Simplifying x = -33.15521837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.65521837, -33.15521837}

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