2x^2-5x-72=

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Solution for 2x^2-5x-72= equation:


Simplifying
2x2 + -5x + -72 = 0

Reorder the terms:
-72 + -5x + 2x2 = 0

Solving
-72 + -5x + 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 + -2.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -2.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -2.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -2.5x + x2 = 0 + 36
-2.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-2.5x + x2 = 36

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 36 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 36 + 1.5625

Combine like terms: 36 + 1.5625 = 37.5625
1.5625 + -2.5x + x2 = 37.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 37.5625

Calculate the square root of the right side: 6.128825336

Break this problem into two subproblems by setting 
(x + -1.25) equal to 6.128825336 and -6.128825336.

Subproblem 1

x + -1.25 = 6.128825336 Simplifying x + -1.25 = 6.128825336 Reorder the terms: -1.25 + x = 6.128825336 Solving -1.25 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 6.128825336 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.128825336 + 1.25 x = 6.128825336 + 1.25 Combine like terms: 6.128825336 + 1.25 = 7.378825336 x = 7.378825336 Simplifying x = 7.378825336

Subproblem 2

x + -1.25 = -6.128825336 Simplifying x + -1.25 = -6.128825336 Reorder the terms: -1.25 + x = -6.128825336 Solving -1.25 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -6.128825336 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.128825336 + 1.25 x = -6.128825336 + 1.25 Combine like terms: -6.128825336 + 1.25 = -4.878825336 x = -4.878825336 Simplifying x = -4.878825336

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.378825336, -4.878825336}

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