x^2-64x+576=0

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Solution for x^2-64x+576=0 equation:


Simplifying
x2 + -64x + 576 = 0

Reorder the terms:
576 + -64x + x2 = 0

Solving
576 + -64x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-576' to each side of the equation.
576 + -64x + -576 + x2 = 0 + -576

Reorder the terms:
576 + -576 + -64x + x2 = 0 + -576

Combine like terms: 576 + -576 = 0
0 + -64x + x2 = 0 + -576
-64x + x2 = 0 + -576

Combine like terms: 0 + -576 = -576
-64x + x2 = -576

The x term is -64x.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64x + 1024 + x2 = -576 + 1024

Reorder the terms:
1024 + -64x + x2 = -576 + 1024

Combine like terms: -576 + 1024 = 448
1024 + -64x + x2 = 448

Factor a perfect square on the left side:
(x + -32)(x + -32) = 448

Calculate the square root of the right side: 21.166010489

Break this problem into two subproblems by setting 
(x + -32) equal to 21.166010489 and -21.166010489.

Subproblem 1

x + -32 = 21.166010489 Simplifying x + -32 = 21.166010489 Reorder the terms: -32 + x = 21.166010489 Solving -32 + x = 21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 21.166010489 + 32 Combine like terms: -32 + 32 = 0 0 + x = 21.166010489 + 32 x = 21.166010489 + 32 Combine like terms: 21.166010489 + 32 = 53.166010489 x = 53.166010489 Simplifying x = 53.166010489

Subproblem 2

x + -32 = -21.166010489 Simplifying x + -32 = -21.166010489 Reorder the terms: -32 + x = -21.166010489 Solving -32 + x = -21.166010489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -21.166010489 + 32 Combine like terms: -32 + 32 = 0 0 + x = -21.166010489 + 32 x = -21.166010489 + 32 Combine like terms: -21.166010489 + 32 = 10.833989511 x = 10.833989511 Simplifying x = 10.833989511

Solution

The solution to the problem is based on the solutions from the subproblems. x = {53.166010489, 10.833989511}

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