# x(x-8)=1089

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## Solution for x(x-8)=1089 equation:

Simplifying
x(x + -8) = 1089
Reorder the terms:
x(-8 + x) = 1089
(-8 * x + x * x) = 1089
(-8x + x2) = 1089
Solving
-8x + x2 = 1089
Solving for variable 'x'.
Reorder the terms:
-1089 + -8x + x2 = 1089 + -1089
Combine like terms: 1089 + -1089 = 0
-1089 + -8x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '1089' to each side of the equation.
-1089 + -8x + 1089 + x2 = 0 + 1089
Reorder the terms:
-1089 + 1089 + -8x + x2 = 0 + 1089
Combine like terms: -1089 + 1089 = 0
0 + -8x + x2 = 0 + 1089
-8x + x2 = 0 + 1089
Combine like terms: 0 + 1089 = 1089
-8x + x2 = 1089
The x term is -8x. Take half its coefficient (-4).
Square it (16) and add it to both sides.
Add '16' to each side of the equation.
-8x + 16 + x2 = 1089 + 16
Reorder the terms:
16 + -8x + x2 = 1089 + 16
Combine like terms: 1089 + 16 = 1105
16 + -8x + x2 = 1105
Factor a perfect square on the left side:
(x + -4)(x + -4) = 1105
Calculate the square root of the right side: 33.241540277
Break this problem into two subproblems by setting
(x + -4) equal to 33.241540277 and -33.241540277.
Subproblem 1x + -4 = 33.241540277
Simplifying
x + -4 = 33.241540277
Reorder the terms:
-4 + x = 33.241540277
Solving
-4 + x = 33.241540277
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + x = 33.241540277 + 4
Combine like terms: -4 + 4 = 0
0 + x = 33.241540277 + 4
x = 33.241540277 + 4
Combine like terms: 33.241540277 + 4 = 37.241540277
x = 37.241540277
Simplifying
x = 37.241540277
Subproblem 2x + -4 = -33.241540277
Simplifying
x + -4 = -33.241540277
Reorder the terms:
-4 + x = -33.241540277
Solving
-4 + x = -33.241540277
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4' to each side of the equation.
-4 + 4 + x = -33.241540277 + 4
Combine like terms: -4 + 4 = 0
0 + x = -33.241540277 + 4
x = -33.241540277 + 4
Combine like terms: -33.241540277 + 4 = -29.241540277
x = -29.241540277
Simplifying
x = -29.241540277
SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {37.241540277, -29.241540277}`

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