225=x^2-50x

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Solution for 225=x^2-50x equation:


Simplifying
225 = x2 + -50x

Reorder the terms:
225 = -50x + x2

Solving
225 = -50x + x2

Solving for variable 'x'.

Reorder the terms:
225 + 50x + -1x2 = -50x + 50x + x2 + -1x2

Combine like terms: -50x + 50x = 0
225 + 50x + -1x2 = 0 + x2 + -1x2
225 + 50x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
225 + 50x + -1x2 = 0

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

Divide each side by '-1'.
-225 + -50x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -50x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -50x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -50x + x2 = 0 + 225
-50x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-50x + x2 = 225

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 = 225 + 625

Reorder the terms:
625 + -50x + x2 = 225 + 625

Combine like terms: 225 + 625 = 850
625 + -50x + x2 = 850

Factor a perfect square on the left side:
(x + -25)(x + -25) = 850

Calculate the square root of the right side: 29.154759474

Break this problem into two subproblems by setting 
(x + -25) equal to 29.154759474 and -29.154759474.

Subproblem 1

x + -25 = 29.154759474 Simplifying x + -25 = 29.154759474 Reorder the terms: -25 + x = 29.154759474 Solving -25 + x = 29.154759474 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 = 29.154759474 + 25 Combine like terms: -25 + 25 = 0 0 + x = 29.154759474 + 25 x = 29.154759474 + 25 Combine like terms: 29.154759474 + 25 = 54.154759474 x = 54.154759474 Simplifying x = 54.154759474

Subproblem 2

x + -25 = -29.154759474 Simplifying x + -25 = -29.154759474 Reorder the terms: -25 + x = -29.154759474 Solving -25 + x = -29.154759474 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 = -29.154759474 + 25 Combine like terms: -25 + 25 = 0 0 + x = -29.154759474 + 25 x = -29.154759474 + 25 Combine like terms: -29.154759474 + 25 = -4.154759474 x = -4.154759474 Simplifying x = -4.154759474

Solution

The solution to the problem is based on the solutions from the subproblems. x = {54.154759474, -4.154759474}

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