x(x-50)-36=0

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Solution for x(x-50)-36=0 equation:


Simplifying
x(x + -50) + -36 = 0

Reorder the terms:
x(-50 + x) + -36 = 0
(-50 * x + x * x) + -36 = 0
(-50x + x2) + -36 = 0

Reorder the terms:
-36 + -50x + x2 = 0

Solving
-36 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -50x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -50x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -50x + x2 = 0 + 36
-50x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-50x + x2 = 36

The x term is -50x.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50x + 625 + x2 = 36 + 625

Reorder the terms:
625 + -50x + x2 = 36 + 625

Combine like terms: 36 + 625 = 661
625 + -50x + x2 = 661

Factor a perfect square on the left side:
(x + -25)(x + -25) = 661

Calculate the square root of the right side: 25.709920264

Break this problem into two subproblems by setting 
(x + -25) equal to 25.709920264 and -25.709920264.

Subproblem 1

x + -25 = 25.709920264 Simplifying x + -25 = 25.709920264 Reorder the terms: -25 + x = 25.709920264 Solving -25 + x = 25.709920264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 25.709920264 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.709920264 + 25 x = 25.709920264 + 25 Combine like terms: 25.709920264 + 25 = 50.709920264 x = 50.709920264 Simplifying x = 50.709920264

Subproblem 2

x + -25 = -25.709920264 Simplifying x + -25 = -25.709920264 Reorder the terms: -25 + x = -25.709920264 Solving -25 + x = -25.709920264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -25.709920264 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.709920264 + 25 x = -25.709920264 + 25 Combine like terms: -25.709920264 + 25 = -0.709920264 x = -0.709920264 Simplifying x = -0.709920264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50.709920264, -0.709920264}

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