x(x+5)=35

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Solution for x(x+5)=35 equation: 


Simplifying
x(x + 5) = 35

Reorder the terms:
x(5 + x) = 35
(5 * x + x * x) = 35
(5x + x2) = 35

Solving
5x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + 5x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 5x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 5x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 5x + x2 = 0 + 35
5x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
5x + x2 = 35

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 = 35 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 35 + 6.25

Combine like terms: 35 + 6.25 = 41.25
6.25 + 5x + x2 = 41.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 2.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + 2.5 = 6.422616289

Simplifying
x + 2.5 = 6.422616289

Reorder the terms:
2.5 + x = 6.422616289

Solving
2.5 + x = 6.422616289

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 = 6.422616289 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 6.422616289 + -2.5
x = 6.422616289 + -2.5

Combine like terms: 6.422616289 + -2.5 = 3.922616289
x = 3.922616289

Simplifying
x = 3.922616289


Subproblem 2
x + 2.5 = -6.422616289

Simplifying
x + 2.5 = -6.422616289

Reorder the terms:
2.5 + x = -6.422616289

Solving
2.5 + x = -6.422616289

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 = -6.422616289 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -6.422616289 + -2.5
x = -6.422616289 + -2.5

Combine like terms: -6.422616289 + -2.5 = -8.922616289
x = -8.922616289

Simplifying
x = -8.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.922616289, -8.922616289}

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