x^2-144x+1024=0

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Solution for x^2-144x+1024=0 equation:


Simplifying
x2 + -144x + 1024 = 0

Reorder the terms:
1024 + -144x + x2 = 0

Solving
1024 + -144x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1024' to each side of the equation.
1024 + -144x + -1024 + x2 = 0 + -1024

Reorder the terms:
1024 + -1024 + -144x + x2 = 0 + -1024

Combine like terms: 1024 + -1024 = 0
0 + -144x + x2 = 0 + -1024
-144x + x2 = 0 + -1024

Combine like terms: 0 + -1024 = -1024
-144x + x2 = -1024

The x term is -144x.  Take half its coefficient (-72).
Square it (5184) and add it to both sides.

Add '5184' to each side of the equation.
-144x + 5184 + x2 = -1024 + 5184

Reorder the terms:
5184 + -144x + x2 = -1024 + 5184

Combine like terms: -1024 + 5184 = 4160
5184 + -144x + x2 = 4160

Factor a perfect square on the left side:
(x + -72)(x + -72) = 4160

Calculate the square root of the right side: 64.498061986

Break this problem into two subproblems by setting 
(x + -72) equal to 64.498061986 and -64.498061986.

Subproblem 1

x + -72 = 64.498061986 Simplifying x + -72 = 64.498061986 Reorder the terms: -72 + x = 64.498061986 Solving -72 + x = 64.498061986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = 64.498061986 + 72 Combine like terms: -72 + 72 = 0 0 + x = 64.498061986 + 72 x = 64.498061986 + 72 Combine like terms: 64.498061986 + 72 = 136.498061986 x = 136.498061986 Simplifying x = 136.498061986

Subproblem 2

x + -72 = -64.498061986 Simplifying x + -72 = -64.498061986 Reorder the terms: -72 + x = -64.498061986 Solving -72 + x = -64.498061986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = -64.498061986 + 72 Combine like terms: -72 + 72 = 0 0 + x = -64.498061986 + 72 x = -64.498061986 + 72 Combine like terms: -64.498061986 + 72 = 7.501938014 x = 7.501938014 Simplifying x = 7.501938014

Solution

The solution to the problem is based on the solutions from the subproblems. x = {136.498061986, 7.501938014}

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