-x^2+74x+2596=0

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Solution for -x^2+74x+2596=0 equation:


Simplifying
-1x2 + 74x + 2596 = 0

Reorder the terms:
2596 + 74x + -1x2 = 0

Solving
2596 + 74x + -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'.
-2596 + -74x + x2 = 0

Move the constant term to the right:

Add '2596' to each side of the equation.
-2596 + -74x + 2596 + x2 = 0 + 2596

Reorder the terms:
-2596 + 2596 + -74x + x2 = 0 + 2596

Combine like terms: -2596 + 2596 = 0
0 + -74x + x2 = 0 + 2596
-74x + x2 = 0 + 2596

Combine like terms: 0 + 2596 = 2596
-74x + x2 = 2596

The x term is -74x.  Take half its coefficient (-37).
Square it (1369) and add it to both sides.

Add '1369' to each side of the equation.
-74x + 1369 + x2 = 2596 + 1369

Reorder the terms:
1369 + -74x + x2 = 2596 + 1369

Combine like terms: 2596 + 1369 = 3965
1369 + -74x + x2 = 3965

Factor a perfect square on the left side:
(x + -37)(x + -37) = 3965

Calculate the square root of the right side: 62.968245966

Break this problem into two subproblems by setting 
(x + -37) equal to 62.968245966 and -62.968245966.

Subproblem 1

x + -37 = 62.968245966 Simplifying x + -37 = 62.968245966 Reorder the terms: -37 + x = 62.968245966 Solving -37 + x = 62.968245966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = 62.968245966 + 37 Combine like terms: -37 + 37 = 0 0 + x = 62.968245966 + 37 x = 62.968245966 + 37 Combine like terms: 62.968245966 + 37 = 99.968245966 x = 99.968245966 Simplifying x = 99.968245966

Subproblem 2

x + -37 = -62.968245966 Simplifying x + -37 = -62.968245966 Reorder the terms: -37 + x = -62.968245966 Solving -37 + x = -62.968245966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = -62.968245966 + 37 Combine like terms: -37 + 37 = 0 0 + x = -62.968245966 + 37 x = -62.968245966 + 37 Combine like terms: -62.968245966 + 37 = -25.968245966 x = -25.968245966 Simplifying x = -25.968245966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {99.968245966, -25.968245966}

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