(x+5)x+7=735

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Solution for (x+5)x+7=735 equation: 


Simplifying
(x + 5) * x + 7 = 735

Reorder the terms:
(5 + x) * x + 7 = 735

Reorder the terms for easier multiplication:
x(5 + x) + 7 = 735
(5 * x + x * x) + 7 = 735
(5x + x2) + 7 = 735

Reorder the terms:
7 + 5x + x2 = 735

Solving
7 + 5x + x2 = 735

Solving for variable 'x'.

Reorder the terms:
7 + -735 + 5x + x2 = 735 + -735

Combine like terms: 7 + -735 = -728
-728 + 5x + x2 = 735 + -735

Combine like terms: 735 + -735 = 0
-728 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '728' to each side of the equation.
-728 + 5x + 728 + x2 = 0 + 728

Reorder the terms:
-728 + 728 + 5x + x2 = 0 + 728

Combine like terms: -728 + 728 = 0
0 + 5x + x2 = 0 + 728
5x + x2 = 0 + 728

Combine like terms: 0 + 728 = 728
5x + x2 = 728

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 728 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 728 + 6.25

Combine like terms: 728 + 6.25 = 734.25
6.25 + 5x + x2 = 734.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 734.25

Calculate the square root of the right side: 27.09704781

Break this problem into two subproblems by setting 
(x + 2.5) equal to 27.09704781 and -27.09704781.


Subproblem 1
x + 2.5 = 27.09704781

Simplifying
x + 2.5 = 27.09704781

Reorder the terms:
2.5 + x = 27.09704781

Solving
2.5 + x = 27.09704781

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 27.09704781 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 27.09704781 + -2.5
x = 27.09704781 + -2.5

Combine like terms: 27.09704781 + -2.5 = 24.59704781
x = 24.59704781

Simplifying
x = 24.59704781


Subproblem 2
x + 2.5 = -27.09704781

Simplifying
x + 2.5 = -27.09704781

Reorder the terms:
2.5 + x = -27.09704781

Solving
2.5 + x = -27.09704781

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -27.09704781 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -27.09704781 + -2.5
x = -27.09704781 + -2.5

Combine like terms: -27.09704781 + -2.5 = -29.59704781
x = -29.59704781

Simplifying
x = -29.59704781


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.59704781, -29.59704781}

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