x(64-x)=126

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Solution for x(64-x)=126 equation:


Simplifying
x(64 + -1x) = 126
(64 * x + -1x * x) = 126
(64x + -1x2) = 126

Solving
64x + -1x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 64x + -1x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 64x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
126 + -64x + x2 = 0

Move the constant term to the right:

Add '-126' to each side of the equation.
126 + -64x + -126 + x2 = 0 + -126

Reorder the terms:
126 + -126 + -64x + x2 = 0 + -126

Combine like terms: 126 + -126 = 0
0 + -64x + x2 = 0 + -126
-64x + x2 = 0 + -126

Combine like terms: 0 + -126 = -126
-64x + x2 = -126

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 = -126 + 1024

Reorder the terms:
1024 + -64x + x2 = -126 + 1024

Combine like terms: -126 + 1024 = 898
1024 + -64x + x2 = 898

Factor a perfect square on the left side:
(x + -32)(x + -32) = 898

Calculate the square root of the right side: 29.966648128

Break this problem into two subproblems by setting 
(x + -32) equal to 29.966648128 and -29.966648128.

Subproblem 1

x + -32 = 29.966648128 Simplifying x + -32 = 29.966648128 Reorder the terms: -32 + x = 29.966648128 Solving -32 + x = 29.966648128 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 = 29.966648128 + 32 Combine like terms: -32 + 32 = 0 0 + x = 29.966648128 + 32 x = 29.966648128 + 32 Combine like terms: 29.966648128 + 32 = 61.966648128 x = 61.966648128 Simplifying x = 61.966648128

Subproblem 2

x + -32 = -29.966648128 Simplifying x + -32 = -29.966648128 Reorder the terms: -32 + x = -29.966648128 Solving -32 + x = -29.966648128 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 = -29.966648128 + 32 Combine like terms: -32 + 32 = 0 0 + x = -29.966648128 + 32 x = -29.966648128 + 32 Combine like terms: -29.966648128 + 32 = 2.033351872 x = 2.033351872 Simplifying x = 2.033351872

Solution

The solution to the problem is based on the solutions from the subproblems. x = {61.966648128, 2.033351872}

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