2x^2-25x-72=

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Solution for 2x^2-25x-72= equation:


Simplifying
2x2 + -25x + -72 = 0

Reorder the terms:
-72 + -25x + 2x2 = 0

Solving
-72 + -25x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-36 + -12.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -12.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -12.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -12.5x + x2 = 0 + 36
-12.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-12.5x + x2 = 36

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 36 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 36 + 39.0625

Combine like terms: 36 + 39.0625 = 75.0625
39.0625 + -12.5x + x2 = 75.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 75.0625

Calculate the square root of the right side: 8.663861726

Break this problem into two subproblems by setting 
(x + -6.25) equal to 8.663861726 and -8.663861726.

Subproblem 1

x + -6.25 = 8.663861726 Simplifying x + -6.25 = 8.663861726 Reorder the terms: -6.25 + x = 8.663861726 Solving -6.25 + x = 8.663861726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 8.663861726 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 8.663861726 + 6.25 x = 8.663861726 + 6.25 Combine like terms: 8.663861726 + 6.25 = 14.913861726 x = 14.913861726 Simplifying x = 14.913861726

Subproblem 2

x + -6.25 = -8.663861726 Simplifying x + -6.25 = -8.663861726 Reorder the terms: -6.25 + x = -8.663861726 Solving -6.25 + x = -8.663861726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -8.663861726 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -8.663861726 + 6.25 x = -8.663861726 + 6.25 Combine like terms: -8.663861726 + 6.25 = -2.413861726 x = -2.413861726 Simplifying x = -2.413861726

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.913861726, -2.413861726}

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