4x+x(x-69)=705

Solution for 4x+x(x-69)=705 equation:

Simplifying
4x + x(x + -69) = 705

Reorder the terms:
4x + x(-69 + x) = 705
4x + (-69 * x + x * x) = 705
4x + (-69x + x2) = 705

Combine like terms: 4x + -69x = -65x
-65x + x2 = 705

Solving
-65x + x2 = 705

Solving for variable 'x'.

Reorder the terms:
-705 + -65x + x2 = 705 + -705

Combine like terms: 705 + -705 = 0
-705 + -65x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '705' to each side of the equation.
-705 + -65x + 705 + x2 = 0 + 705

Reorder the terms:
-705 + 705 + -65x + x2 = 0 + 705

Combine like terms: -705 + 705 = 0
0 + -65x + x2 = 0 + 705
-65x + x2 = 0 + 705

Combine like terms: 0 + 705 = 705
-65x + x2 = 705

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = 705 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = 705 + 1056.25

Combine like terms: 705 + 1056.25 = 1761.25
1056.25 + -65x + x2 = 1761.25

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 1761.25

Calculate the square root of the right side: 41.967249135

Break this problem into two subproblems by setting 
(x + -32.5) equal to 41.967249135 and -41.967249135.

Subproblem 1
x + -32.5 = 41.967249135

Simplifying
x + -32.5 = 41.967249135

Reorder the terms:
-32.5 + x = 41.967249135

Solving
-32.5 + x = 41.967249135

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = 41.967249135 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = 41.967249135 + 32.5
x = 41.967249135 + 32.5

Combine like terms: 41.967249135 + 32.5 = 74.467249135
x = 74.467249135

Simplifying
x = 74.467249135

Subproblem 2
x + -32.5 = -41.967249135

Simplifying
x + -32.5 = -41.967249135

Reorder the terms:
-32.5 + x = -41.967249135

Solving
-32.5 + x = -41.967249135

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = -41.967249135 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = -41.967249135 + 32.5
x = -41.967249135 + 32.5

Combine like terms: -41.967249135 + 32.5 = -9.467249135
x = -9.467249135

Simplifying
x = -9.467249135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {74.467249135, -9.467249135}