-x^2+948x-2500=0

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Solution for -x^2+948x-2500=0 equation:


Simplifying
-1x2 + 948x + -2500 = 0

Reorder the terms:
-2500 + 948x + -1x2 = 0

Solving
-2500 + 948x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
2500 + -948x + x2 = 0

Move the constant term to the right:

Add '-2500' to each side of the equation.
2500 + -948x + -2500 + x2 = 0 + -2500

Reorder the terms:
2500 + -2500 + -948x + x2 = 0 + -2500

Combine like terms: 2500 + -2500 = 0
0 + -948x + x2 = 0 + -2500
-948x + x2 = 0 + -2500

Combine like terms: 0 + -2500 = -2500
-948x + x2 = -2500

The x term is -948x.  Take half its coefficient (-474).
Square it (224676) and add it to both sides.

Add '224676' to each side of the equation.
-948x + 224676 + x2 = -2500 + 224676

Reorder the terms:
224676 + -948x + x2 = -2500 + 224676

Combine like terms: -2500 + 224676 = 222176
224676 + -948x + x2 = 222176

Factor a perfect square on the left side:
(x + -474)(x + -474) = 222176

Calculate the square root of the right side: 471.355492171

Break this problem into two subproblems by setting 
(x + -474) equal to 471.355492171 and -471.355492171.

Subproblem 1

x + -474 = 471.355492171 Simplifying x + -474 = 471.355492171 Reorder the terms: -474 + x = 471.355492171 Solving -474 + x = 471.355492171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '474' to each side of the equation. -474 + 474 + x = 471.355492171 + 474 Combine like terms: -474 + 474 = 0 0 + x = 471.355492171 + 474 x = 471.355492171 + 474 Combine like terms: 471.355492171 + 474 = 945.355492171 x = 945.355492171 Simplifying x = 945.355492171

Subproblem 2

x + -474 = -471.355492171 Simplifying x + -474 = -471.355492171 Reorder the terms: -474 + x = -471.355492171 Solving -474 + x = -471.355492171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '474' to each side of the equation. -474 + 474 + x = -471.355492171 + 474 Combine like terms: -474 + 474 = 0 0 + x = -471.355492171 + 474 x = -471.355492171 + 474 Combine like terms: -471.355492171 + 474 = 2.644507829 x = 2.644507829 Simplifying x = 2.644507829

Solution

The solution to the problem is based on the solutions from the subproblems. x = {945.355492171, 2.644507829}

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