x(x+5)=3450

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Solution for x(x+5)=3450 equation: 


Simplifying
x(x + 5) = 3450

Reorder the terms:
x(5 + x) = 3450
(5 * x + x * x) = 3450
(5x + x2) = 3450

Solving
5x + x2 = 3450

Solving for variable 'x'.

Reorder the terms:
-3450 + 5x + x2 = 3450 + -3450

Combine like terms: 3450 + -3450 = 0
-3450 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3450' to each side of the equation.
-3450 + 5x + 3450 + x2 = 0 + 3450

Reorder the terms:
-3450 + 3450 + 5x + x2 = 0 + 3450

Combine like terms: -3450 + 3450 = 0
0 + 5x + x2 = 0 + 3450
5x + x2 = 0 + 3450

Combine like terms: 0 + 3450 = 3450
5x + x2 = 3450

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 = 3450 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 3450 + 6.25

Combine like terms: 3450 + 6.25 = 3456.25
6.25 + 5x + x2 = 3456.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3456.25

Calculate the square root of the right side: 58.789880082

Break this problem into two subproblems by setting 
(x + 2.5) equal to 58.789880082 and -58.789880082.


Subproblem 1
x + 2.5 = 58.789880082

Simplifying
x + 2.5 = 58.789880082

Reorder the terms:
2.5 + x = 58.789880082

Solving
2.5 + x = 58.789880082

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 = 58.789880082 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 58.789880082 + -2.5
x = 58.789880082 + -2.5

Combine like terms: 58.789880082 + -2.5 = 56.289880082
x = 56.289880082

Simplifying
x = 56.289880082


Subproblem 2
x + 2.5 = -58.789880082

Simplifying
x + 2.5 = -58.789880082

Reorder the terms:
2.5 + x = -58.789880082

Solving
2.5 + x = -58.789880082

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 = -58.789880082 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -58.789880082 + -2.5
x = -58.789880082 + -2.5

Combine like terms: -58.789880082 + -2.5 = -61.289880082
x = -61.289880082

Simplifying
x = -61.289880082


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {56.289880082, -61.289880082}

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