x^2-50x+189=0

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Solution for x^2-50x+189=0 equation:


Simplifying
x2 + -50x + 189 = 0

Reorder the terms:
189 + -50x + x2 = 0

Solving
189 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-189' to each side of the equation.
189 + -50x + -189 + x2 = 0 + -189

Reorder the terms:
189 + -189 + -50x + x2 = 0 + -189

Combine like terms: 189 + -189 = 0
0 + -50x + x2 = 0 + -189
-50x + x2 = 0 + -189

Combine like terms: 0 + -189 = -189
-50x + x2 = -189

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 = -189 + 625

Reorder the terms:
625 + -50x + x2 = -189 + 625

Combine like terms: -189 + 625 = 436
625 + -50x + x2 = 436

Factor a perfect square on the left side:
(x + -25)(x + -25) = 436

Calculate the square root of the right side: 20.880613018

Break this problem into two subproblems by setting 
(x + -25) equal to 20.880613018 and -20.880613018.

Subproblem 1

x + -25 = 20.880613018 Simplifying x + -25 = 20.880613018 Reorder the terms: -25 + x = 20.880613018 Solving -25 + x = 20.880613018 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 = 20.880613018 + 25 Combine like terms: -25 + 25 = 0 0 + x = 20.880613018 + 25 x = 20.880613018 + 25 Combine like terms: 20.880613018 + 25 = 45.880613018 x = 45.880613018 Simplifying x = 45.880613018

Subproblem 2

x + -25 = -20.880613018 Simplifying x + -25 = -20.880613018 Reorder the terms: -25 + x = -20.880613018 Solving -25 + x = -20.880613018 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 = -20.880613018 + 25 Combine like terms: -25 + 25 = 0 0 + x = -20.880613018 + 25 x = -20.880613018 + 25 Combine like terms: -20.880613018 + 25 = 4.119386982 x = 4.119386982 Simplifying x = 4.119386982

Solution

The solution to the problem is based on the solutions from the subproblems. x = {45.880613018, 4.119386982}

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