4x^2-5x-72=0

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Solution for 4x^2-5x-72=0 equation: 


Simplifying
4x2 + -5x + -72 = 0

Reorder the terms:
-72 + -5x + 4x2 = 0

Solving
-72 + -5x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-18 + -1.25x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1.25x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -1.25x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1.25x + x2 = 0 + 18
-1.25x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1.25x + x2 = 18

The x term is -1.25x.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x + 0.390625 + x2 = 18 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 18 + 0.390625

Combine like terms: 18 + 0.390625 = 18.390625
0.390625 + -1.25x + x2 = 18.390625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 18.390625

Calculate the square root of the right side: 4.2884292

Break this problem into two subproblems by setting 
(x + -0.625) equal to 4.2884292 and -4.2884292.


Subproblem 1
x + -0.625 = 4.2884292

Simplifying
x + -0.625 = 4.2884292

Reorder the terms:
-0.625 + x = 4.2884292

Solving
-0.625 + x = 4.2884292

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = 4.2884292 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = 4.2884292 + 0.625
x = 4.2884292 + 0.625

Combine like terms: 4.2884292 + 0.625 = 4.9134292
x = 4.9134292

Simplifying
x = 4.9134292


Subproblem 2
x + -0.625 = -4.2884292

Simplifying
x + -0.625 = -4.2884292

Reorder the terms:
-0.625 + x = -4.2884292

Solving
-0.625 + x = -4.2884292

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.625' to each side of the equation.
-0.625 + 0.625 + x = -4.2884292 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + x = -4.2884292 + 0.625
x = -4.2884292 + 0.625

Combine like terms: -4.2884292 + 0.625 = -3.6634292
x = -3.6634292

Simplifying
x = -3.6634292


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.9134292, -3.6634292}

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