x^2-50x+288=0

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Solution for x^2-50x+288=0 equation:


Simplifying
x2 + -50x + 288 = 0

Reorder the terms:
288 + -50x + x2 = 0

Solving
288 + -50x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-288' to each side of the equation.
288 + -50x + -288 + x2 = 0 + -288

Reorder the terms:
288 + -288 + -50x + x2 = 0 + -288

Combine like terms: 288 + -288 = 0
0 + -50x + x2 = 0 + -288
-50x + x2 = 0 + -288

Combine like terms: 0 + -288 = -288
-50x + x2 = -288

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 = -288 + 625

Reorder the terms:
625 + -50x + x2 = -288 + 625

Combine like terms: -288 + 625 = 337
625 + -50x + x2 = 337

Factor a perfect square on the left side:
(x + -25)(x + -25) = 337

Calculate the square root of the right side: 18.357559751

Break this problem into two subproblems by setting 
(x + -25) equal to 18.357559751 and -18.357559751.

Subproblem 1

x + -25 = 18.357559751 Simplifying x + -25 = 18.357559751 Reorder the terms: -25 + x = 18.357559751 Solving -25 + x = 18.357559751 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 = 18.357559751 + 25 Combine like terms: -25 + 25 = 0 0 + x = 18.357559751 + 25 x = 18.357559751 + 25 Combine like terms: 18.357559751 + 25 = 43.357559751 x = 43.357559751 Simplifying x = 43.357559751

Subproblem 2

x + -25 = -18.357559751 Simplifying x + -25 = -18.357559751 Reorder the terms: -25 + x = -18.357559751 Solving -25 + x = -18.357559751 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 = -18.357559751 + 25 Combine like terms: -25 + 25 = 0 0 + x = -18.357559751 + 25 x = -18.357559751 + 25 Combine like terms: -18.357559751 + 25 = 6.642440249 x = 6.642440249 Simplifying x = 6.642440249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {43.357559751, 6.642440249}

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