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 1

x + -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 2

x + -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

Solution

The solution to the problem is based on the solutions from the subproblems. x = {37.241540277, -29.241540277}

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